<image_1>Circle $O$ has a radius of 13 inches. Radius $\\overline{O B}$ is perpendicular to chord $\\overline{C D}$ which is 24 inches long.\r\nFind OX\n<image><image_2>Find the area of $▱ JKLM$."},"answer":{"kind":"string","value":"5\n24"}}}],"truncated":false,"partial":false},"paginationData":{"pageIndex":0,"numItemsPerPage":100,"numTotalItems":300,"offset":0,"length":100}},"jwt":"eyJhbGciOiJFZERTQSJ9.eyJyZWFkIjp0cnVlLCJwZXJtaXNzaW9ucyI6eyJyZXBvLmNvbnRlbnQucmVhZCI6dHJ1ZX0sImlhdCI6MTc3NjUyNjUyNywic3ViIjoiL2RhdGFzZXRzL1RpZ2VyTEhIL2dlbzNrdGVzdCIsImV4cCI6MTc3NjUzMDEyNywiaXNzIjoiaHR0cHM6Ly9odWdnaW5nZmFjZS5jbyJ9.gWt00RTjGg61AmZgMKKOy0IvqzDs3F8wYas_BB9adN9SQb1ndR5i14CkxMqiarEuhTFQ0sTekAewHKPf5XywAg","displayUrls":true,"splitSizeSummaries":[{"config":"default","split":"test","numRows":300,"numBytesParquet":11322067}]},"discussionsStats":{"closed":0,"open":1,"total":1},"fullWidth":true,"hasGatedAccess":true,"hasFullAccess":true,"isEmbedded":false,"savedQueries":{"community":[],"user":[]}}">
images listlengths 2 2 | problem stringlengths 46 412 | answer stringlengths 3 33 |
|---|---|---|
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAASkAAAEJCAYAAADINdG0AAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAACjbSURBVHhe7Z3/cxTnnefzJ9wv9zMuCSjbhQPYprzlL7hMYWxTa5ajMEuOs8HBNj6fkb0+cFwH9h2wScCVBV8MOa82ZZFk5aQEG+GswWVt1vLFckrkmNjCQTHCAYIcaRGxbGCFMBLzuXnP9CM+anXP9Mz0l2d63q+qpxA9o9FM99Ov/jyf59PPfE0I... | <image><image_1>Chords $\overline{A C}$ and $\overline{D F}$ are equidistant from the center. If the radius of $\odot G$ is 26 find $A C$
<image><image_2>Find the length of $\widehat {ZY}$. Round to the nearest hundredth. | 48
7.85 |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAZQAAACiCAYAAABmkTukAAABRGlDQ1BJQ0MgUHJvZmlsZQAAKJFjYGASSSwoyGFhYGDIzSspCnJ3UoiIjFJgf8LAzCAKhLwMyonJxQWOAQE+QCUMMBoVfLvGwAiiL+uCzOKK+Han7EqwsuVDi8OzwwVXYqpHAVwpqcXJQPoPEKcnFxSVMDAwpgDZyuUlBSB2B5AtUgR0FJA9B8ROh7A3gNhJEPYRsJqQIGcg+waQLZCckQg0g/EFkK2ThCSejsSG2gsCvC6uPj4Kwa5G5oaW... | <image><image_1>Find the area of the figure to the nearest tenth.
<image><image_2>If pentagons $A B C D E$ and $P Q R S T$ are similar, find $S R$ | 31.1
4 \frac { 4 } { 11 } |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAo4AAAJBCAYAAADIsDSBAACA6klEQVR4nO3dd3gb15k18DMz6I0gWEWKYq8q7t1ytyWX2I57t9O8iZM49Uvi9J6ss8mmZ1Mc917SbEty771LIgk2kZTYCZAE0YGZ+f4ACIKyypBiAcnzex49G3stGZZAzsF97z1XUFVVBRERERHRfogL/QKIiIiIaHFgcCQiIiIiTRgciYiIiEgTBkciIiIi0oTBkYiIiIg0YXAkIiIiIk0YHImIiIhIEwZHIiIiItKEwZGIiIiINGFwJCIi... | <image><image_1>In $\triangle PQR$, $\overline{ST} \| \overline{R Q}$ . If $PS=12.5$, $SR=5$, and $PT=15$, find $TQ$.
<image><image_2>$a=14, b=48,$ and $c=50$ find $cosA$ | 6
0.96 |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAYIAAADWCAYAAADckoXcAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAABamSURBVHhe7d3/c1RVmsfx/U+YCpiSsqAyUQor4zBD6VrKgouzooCiOFTAWRbxC64l4ODibjEwozKLODI7IOyQYhFEpkRcdLNZRhQYRTJR3GyKkMjXgCwOm0EEYp7tp8NJLp3T6e7bfbvvPef9w6vA9E1Lkvvcz3PuOffkL+TbMwIA8BdBAACeIwgA... | <image><image_1>$\overline{A C}$ is a diagonal of rhombus $A B C D$ If $m \angle C D E$ is $116,$ what is $m \angle A C D ?$
<image><image_2>Use parallelogram $JKLM$ to find $m \angle KLM$ | 58
71 |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAWAAAACzCAYAAAC3vMZ5AAABRGlDQ1BJQ0MgUHJvZmlsZQAAKJFjYGASSSwoyGFhYGDIzSspCnJ3UoiIjFJgf8LAzCAKhLwMyonJxQWOAQE+QCUMMBoVfLvGwAiiL+uCzOKK+Han7EqwsuVDi8OzwwVXYqpHAVwpqcXJQPoPEKcnFxSVMDAwpgDZyuUlBSB2B5AtUgR0FJA9B8ROh7A3gNhJEPYRsJqQIGcg+waQLZCckQg0g/EFkK2ThCSejsSG2gsCvC6uPj4Kwa5G5oaW... | <image><image_1>Find the perimeter of the parallelogram.
<image><image_2>Find x. | 78
5 \sqrt { 3 } |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAhMAAAGACAYAAAAXueBUAAAgAElEQVR4nOzdBZhc1eEF8DO7Y7uz7m7ZZHfj7p4QgrQFihf+lFLq7k4FWkqdOnWKOwVa4u7uK1l3t9lx+b/7ZnZ2AwlZHzu/78tHCCF52bx5c+bee+5VOCXwEeJSFApF0F8DERGRPwnx9gX084VM4wvXQERE5G98JkwIvjAi4AvXQERE5E+U3v403v/7izdxb18LgwQREdHwKXxpzQQRERH5H5+a5iAiIiL/wzBBREREo8IwQURERKPCMEFE... | <image><image_1>Find $PS$.
<image><image_2>In the figure, $m∠1 = 50$ and $m∠3 = 60$. Find the measure of $\angle 8$. | 9
120 |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAcYAAAENCAYAAACVTcVeAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAACEKSURBVHhe7d3/j9XVncdx/4z+hmEqUYOxFYnERcwaY5QgElKIkTSy1VbaLqVfgHRXNOu3VEgrZBWTqnGgq431G9oVGqx1aKHtyIoKBFfGLdsOit1BBoYRhuHLfe9937nnzpnPfO7M/fL5cs75PB/JJ8DMMF/unXNf532+fS4SAABQQzACAGAhGAEA... | <image><image_1>Find x
<image><image_2>Quadrilateral $ABDC$ is a rectangle. If $m\angle1 = 38$, find $m \angle 2$ | 4
52 |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAR8AAAF7CAYAAADrMo8BAAABRmlDQ1BJQ0MgUHJvZmlsZQAAKJFjYGASSSwoyGFhYGDIzSspCnJ3UoiIjFJgf8LAzCDJwM+gz6CZmFxc4BgQ4ANUwgCjUcG3awyMIPqyLsgszeshTVf+lEYatV4+MlVg9wlM9SiAKyW1OBlI/wHi9OSCohIGBsYUIFu5vKQAxO4AskWKgI4CsueA2OkQ9gYQOwnCPgJWExLkDGTfALIFkjMSgWYwvgCydZKQxNOR2FB7QYDXxdXHRyHY1cjc... | <image><image_1>What is the value of $x$ below to the nearest tenth?
<image><image_2>Find $m\angle W$ | 22.5
108 |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAb0AAADeCAYAAACpOd4EAAABRmlDQ1BJQ0MgUHJvZmlsZQAAeJxjYGASSSwoyGFhYGDIzSspCnJ3UoiIjFJgf8LAzCDJwM+gz6CZmFxc4BgQ4ANUwgCjUcG3awyMIPqyLsgszeshTVf+lEYatV4+MlVg9wlM9SiAKyW1OBlI/wHi9OSCohIGBsYUIFu5vKQAxO4AskWKgI4CsueA2OkQ9gYQOwnCPgJWExLkDGTfALIFkjMSgWYwvgCydZKQxNOR2FB7QYDXxdXHRyHY1cjc... | <image><image_1>Express the ratio of $\cos B$ as a decimal to the nearest hundredth.
<image><image_2>Find the measure of $JK$. | 0.38
31 |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAPMAAADVCAYAAACCA8YUAABC00lEQVR4nO19eZxfRZXv9/aWdJJO0p2dLN0mhHQgYmISlbDJpiiIo6KiI6DOOCPqU9/I0/nMk+eMy6gz6Bv5jIIbMDg+UUExiqLIKgSERJaEELLRCWTppDsJNEkn6XTf98ddfqfqnqpT997fr/vXnfvlc+lfblWdOrXcOqdO1anyjh3p8pEXEQXP8Z3+PgoeKIV5UThJ44e/PY+kp+EcaSZ/n0T0GD7A1QjHr89n6iV+wLnsStk41kieXk2J... | <image><image_1>For trapezoid $T R S V, M$ and $N$ are midpoints of the legs. If $T R=32$ and $M N=25,$ find $V S$
<image><image_2>Find $x$ so that each quadrilateral is a parallelogram. | 18
4 |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAA4EAAAGaCAYAAACxJEa9AAAgAElEQVR4nOzdBXhUV+I28Hfc425ESIK7V6CUylZoaal7qW3/23Xfbffb7bq3291CXalQF6rUi7sTIxB3G5c73z03QoBAIUpm3l+fPIXIZEhm7tz3nnPeowrKQERERERERGFBPdR3gIiIiIiIiAYPQyAREREREVEYYQgkIiIiIiIKIwyBREREREREYYQhkIiIiIiIKIwwBBIREREREYURhkAiIiIiIqIwwhBIREREREQURhgCiYiIiIiIwghD... | <image><image_1>Find $WR$.
<image><image_2>Find the value of $x$ | 8
74 |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAQkAAADQCAYAAAAULpQ3AAABRmlDQ1BJQ0MgUHJvZmlsZQAAKJFjYGASSSwoyGFhYGDIzSspCnJ3UoiIjFJgf8LAzCDGIMRgyKCfmFxc4BgQ4ANUwgCjUcG3awyMIPqyLsisB/O42vdrVBiX2l66POt2/ANM9SiAKyW1OBlI/wHi9OSCohIGBsYUIFu5vKQAxO4AskWKgI4CsueA2OkQ9gYQOwnCPgJWExLkDGTfALIFkjMSgWYwvgCydZKQxNOR2FB7QYDXxdXHRyHY1cjc... | <image><image_1>Find the area of the trapezoid.
<image><image_2>The diameters of $\odot A, \odot B,$ and $\odot C$ are 10, 30 and 10 units, respectively. Find ZX if $\overline{A Z} \cong \overline{C W}$ and $C W=2$. | 678.5
3 |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAVIAAAC/CAYAAACseFQHAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAABRBSURBVHhe7d3/bxV1vsdx/5OSHm2UYFCwkRgtycaYKxcrkpUQ+UGuorAkLC4L3NwskgjulZJdIbtA7sWNLXHd7MV1QWNJ5HIpe9Wb6hWXYsrVGtlr0V4tWCi1lFI67zvv0/m009M5p+ecmTNfn49kAp3zpXPamde8P/Oemd4iAABfCFIA8IkgBQCf... | <image><image_1>Find x
<image><image_2>Find x. Round to the nearest tenth. | 6 \sqrt { 6 }
52.5 |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAYwAAACZCAYAAAA8VQ3WAABYlUlEQVR4nO2deXwVRdb3v50NkhC2hD0QMEH2UQRFWYWACiKggIKCgiugj7jho46O4+6j4iivIziOgIDjArjAKCibLLIoAgoIQoIBArKEQAjZCEm/f+Qu3X27+lbfJQTo3+dzk3u7q06d2uucOnVKOVOSo+KG9xsomu/a59ofimIeRhs3WLoiSNBUtSQjROlK8GbBji4Nu7SEfEgm7o++DCTrzZNPRa56AkovFHGl6WszpwkYDp4qO66wvWm6... | <image><image_1>Find $y$ so that each quadrilateral is a parallelogram.
<image><image_2>Find $K J$ if $G J=8, G H=12,$ and $H I=4$ | 31
2 |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAgkAAAHTCAYAAACtL4ssAAAgAElEQVR4nOzdB5xU5bk/8N/M7PTZ3vsubKM3wQI2BLtRgwVLYhLNP+0mN8lNYklMbopppl+TG71pGkXEHrvSUVAMsPRtsL3MbN+dXv/nPTM7u4sDLrCwM7u/7ydEEFhGdvac33nf530eRUACIiIiomMoJ/oFEBERUXRiSCAiIqKIGBKIiIgoIoYEIiIiioghgYiIiCJiSCAiIqKIGBKIiIgoIoYEIiIiioghgYiIiCJiSCAiIqKIGBKIiIgo... | <image><image_1>Find $QP$.
<image><image_2>In $\odot T, Z V=1,$ and $T W=13$. Find XY | 3.6
10 |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAdcAAAGnCAYAAADlph0AAAABRmlDQ1BJQ0MgUHJvZmlsZQAAKJFjYGASSSwoyGFhYGDIzSspCnJ3UoiIjFJgf8LAzMDLwMOgwmCamFxc4BgQ4ANUwgCjUcG3awyMIPqyLsgsiVdHP0z4p9fCYxi/UHqHuw2mehTAlZJanAyk/wBxenJBUQkDA2MKkK1cXlIAYncA2SJFQEcB2XNA7HQIewOInQRhHwGrCQlyBrJvANkCyRmJQDMYXwDZOklI4ulIbKi9IMDr4urjoxDsamRu... | <image><image_1>In the figure, $m∠11 = 62$ and $m∠14 = 38$. Find the measure of $\angle 1$.
<image><image_2>The two polygons are similar. Find UT. | 38
22.5 |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAPIAAAEUCAYAAAARAmuPAAABRmlDQ1BJQ0MgUHJvZmlsZQAAKJFjYGASSSwoyGFhYGDIzSspCnJ3UoiIjFJgf8LAzCDOIMagxMCUmFxc4BgQ4ANUwgCjUcG3awyMIPqyLsgshq8p1i5tGxpuH1q24uOJ7/cw1aMArpTU4mQg/QeI05MLikoYGBhTgGzl8pICELsDyBYpAjoKyJ4DYqdD2BtA7CQI+whYTUiQM5B9A8gWSM5IBJrB+ALI1klCEk9HYkPtBQFeF1cfH4VgVyNz... | <image><image_1>Find the measure of $∠A$ to the nearest tenth.
<image><image_2>Find $m \angle H$. | 41.8
31 |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAYcAAACrCAYAAACNB1CHAAABRmlDQ1BJQ0MgUHJvZmlsZQAAKJFjYGASSSwoyGFhYGDIzSspCnJ3UoiIjFJgf8LAzMDLwMOgwmCamFxc4BgQ4ANUwgCjUcG3awyMIPqyLsgsiVdHP0z4p9fCYxi/UHqHuw2mehTAlZJanAyk/wBxenJBUQkDA2MKkK1cXlIAYncA2SJFQEcB2XNA7HQIewOInQRhHwGrCQlyBrJvANkCyRmJQDMYXwDZOklI4ulIbKi9IMDr4urjoxDsamRu... | <image><image_1>Find $x$.
<image><image_2>$m \widehat{AC}=160$ and $m \angle BEC=38$. What is $m \angle AEB$? | 90
42 |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAv0AAAFKCAYAAACO4eBEAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAC0kSURBVHhe7d0xyyxLfh9gfQN/hBUol0C5ZH0Aif0AC3K+CBacrRU4cLIIgyNLiuRI2nATSTgw2EIbGIMx2sXBgo3ZxTgw2L44sAMHx/yuTl39b93q7uqZnnl7ep4HinPO2zXdPfPOVP26uqbOL30CAAAuTegHAICLE/oBAODihH4AALg4oR8AAC5O... | <image><image_1>A plane travels from Des Moines to Phoenix, on to Atlanta, and back to Des Moines, as shown below. Find the distance in miles from Phoenix to Atlanta if the total trip was 3482 miles.
<image><image_2>Find $x$. | 1591
123 |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAoQAAAFQCAYAAAAm8G/rAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAACAySURBVHhe7d1PqzTnmR/gfJMEnGSGTEae8QwMSFg4gcAM2OMkNg5BxGSRkERxQpDxQnj1oo3wZjJZ2N7IO9sJr5a2YUJmZcFkLTPZy/oC8ic40U869fo+j6q7qv9Ud1U91wU30jmnT/d5+/Sp+vV9Vz31dx4AAOiaQAgA0DmBEACgcwIhAEDnBEIA... | <image><image_1>Solve for x in the figure. Round to the nearest tenth if necessary.
<image><image_2>In the figure, $\overline{A D}$ is perpendicular to $\overline{B C}$ and $\overline{A B}$ is perpendicular to $\overline{A C}$. What is $B C ?$ | 3
20 |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAM4AAADKCAYAAADtjn/SAAABRmlDQ1BJQ0MgUHJvZmlsZQAAeJxjYGASSSwoyGFhYGDIzSspCnJ3UoiIjFJgf8LAzCDGIMRgyKCfmFxc4BgQ4ANUwgCjUcG3awyMIPqyLsisB/O42vdrVBiX2l66POt2/ANM9SiAKyW1OBlI/wHi9OSCohIGBsYUIFu5vKQAxO4AskWKgI4CsueA2OkQ9gYQOwnCPgJWExLkDGTfALIFkjMSgWYwvgCydZKQxNOR2FB7QYDXxdXHRyHY1cjc... | <image><image_1>Find the area of the figure. Round to the nearest tenth.
<image><image_2>If $c=5,$ find $b$ | 30.2
2.5 \sqrt { 3 } |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAb8AAAGnCAYAAAAnllmEAAAgAElEQVR4nOzdZ3CbV7on+D9yJgASzDlKIkXlLDlbzjlnu93tvmFmZ7Zn986H/TRVu7X7Yat25k7dnrm32+2cc7ZlW5atnCiJShTFIOYEIue857xgAClSIilSBIHnV42yRIloiCTe5/2f8BzR7l9+i4nFYiTS6bSQSCQTPqbX6y/7WKbRAKlUOuFjMpkUIpFowscmPz8hhBCymKSFhQWsOE0sahq16rKCpVIpL/uYQqFgH7u80E0ufoQQQkgy... | <image><image_1>Find $z$.
<image><image_2>Find the area of the shaded region. Assume that the polygon is regular unless otherwise stated. Round to the nearest tenth. | 12
216.6 |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAisAAAHqCAYAAADF8g6kAACf20lEQVR4nOzdd3zd5Xn38c/Ze0g6WkdbsizvvW2GF3uPAIFACJDRpu3TPm3TkdE0nelKn7ZpBisJhEAAA2Z5YLDx3nto7z2Ozt6/5w/JsiEYy0P7er9eHSHS0U/inN/5nvu+7utSKYqiIIQQQggxSqlH+gKEEEIIIT6PhBUhhBBCjGoSVoQQQggxqklYEUIIIcSoJmFFCCGEEKOahBUhhBBCjGoSVoQQQggxqklYEUIIIcSoJmFFCCGEEKOa... | <image><image_1>Find $m \angle 2$.
<image><image_2>Find x. Round to the nearest tenth. | 39
5.8 |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAgsAAAIUCAYAAACU32+AAAAgAElEQVR4nOzdd1Sc56Eu+mcYGJjG0OsAaoBQF0KFIsnqsmwncYl7HBclceLYSfbZ66xz1rpn3XvuP/fedc/de7sl3o5bbMfdsR13y7IK6g0VVJGE6L0MMwxTmfu93wwDkqURQjDMwPPLYklCgHCY+b5n3vK8Co8ERERERNcQMd7fABEREYU2hgUiIiIKiGGBiIiIAmJYICIiooAYFoiIiCgghgUiIiIKiGGBiIiIAmJYICIiooAYFoiIiCgg... | <image><image_1>$m$ is the perpendicular bisector of $XZ$, $WZ=14.9$. Find $WX$.
<image><image_2>$m∠9 = 2x - 4$, $m∠10 = 2x + 4$. Find the measure of $∠10$. | 14.9
94 |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAfwAAAFlCAYAAAAOO1qYAAAgAElEQVR4nOzdBXic55U3/P+ARqMZacTMliyZmRlCDjbM2DZJQ4Vtu93d63vf7rfY7bbNNk7SQJtN0obZIceOYyZZZlu2xcwawTC+z32PLENsxyIL5v+7Ll+JlWgykZ95zn2f59znqPwKEBER0aimHuo3QERERIOPAZ+IiCgIMOATEREFAQZ8IiKiIMCAT0REFAQY8ImIiIIAAz4REVEQYMAnIiIKAgz4REREQYABn4iIKAgw4BMREQUBBnwi... | <image><image_1>Find $JL$.
<image><image_2>Find the area of the parallelogram. Round to the nearest tenth if necessary. | 14
91.9 |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAOAAAAEnCAYAAACwt09ZAAABRmlDQ1BJQ0MgUHJvZmlsZQAAKJFjYGASSSwoyGFhYGDIzSspCnJ3UoiIjFJgf8LAzCDOwM8gyyCcmFxc4BgQ4ANUwgCjUcG3awyMIPqyLsis6bce3FrtZzyDZVvGAdHJ7DMw1aMArpTU4mQg/QeI05MLikoYGBhTgGzl8pICELsDyBYpAjoKyJ4DYqdD2BtA7CQI+whYTUiQM5B9A8gWSM5IBJrB+ALI1klCEk9HYkPtBQFeF1cfH4VgVyNz... | <image><image_1>Find x.
<image><image_2>Find $ST$. | 15
19 |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAATYAAAEDCAYAAAC/Cyi3AAABRmlDQ1BJQ0MgUHJvZmlsZQAAKJFjYGASSSwoyGFhYGDIzSspCnJ3UoiIjFJgf8LAzCDOIMSgwiCRmFxc4BgQ4ANUwgCjUcG3awyMIPqyLsisrL0vkkSmTXnwxezN+q1rZI9jqkcBXCmpxclA+g8QpycXFJUwMDCmANnK5SUFIHYHkC1SBHQUkD0HxE6HsDeA2EkQ9hGwmpAgZyD7BpAtkJyRCDSD8QWQrZOEJJ6OxIbaCwK8Lq4+PgrBrkbm... | <image><image_1>Find x.
<image><image_2>Find $EG$ if $G$ is the incenter of $\triangle ABC$. | 18 \sqrt { 6 }
5 |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAUgAAADCCAYAAAArSFs5AAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAABbfSURBVHhe7d3/T1Tnngfw+59gGEuqwYgi0TSKWWO8SpR1SWWJpi0RtdS9fmmLZO8VTdDurZj1S+6Kd69tlnFrs/fivUG9wkbbODZqQrt3WMcGVseU9g6VbqEdQBYp3857zzOcM3OYmcN8Yb6c88z7lZwfODMiDJw3z+c5n+eZn4GIiKJiQBIRmWBA... | <image><image_1>Find $x$ so that each quadrilateral is a parallelogram.
<image><image_2>Find $x$. | 13
3 |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAATgAAAErCAYAAABKPZ9fAAAKuWlDQ1BJQ0MgUHJvZmlsZQAASImVlgdUU1kax+97L52EFnoNvSNFIICU0ANI76ISkkBCCTEhqFiwMDiCY0FEBJQRUSkKjkqRsSKKbVBs2AdERNRxsCAqKvuAJczsnt09+51zc3/58t2vvPNuzh8A8leWUJgBywOQKcgWRfh70eLiE2j4ZwABcoAKcADLYouFjLCwYIDazP53+3gXQJP7LavJXP/++381BQ5XzAYACkM5mSNmZ6J8HF3P2EJR... | <image><image_1>Find x.
<image><image_2>Tangent $\overline{M P}$ is drawn to $\odot O .$ Find $x$ if $M O=20$ | 1
12 |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAcwAAAGjCAYAAACheSUJAAAgAElEQVR4nOy9B3yjZ5n2e0myJcuWZctWd5veMjPJZGoSUkkCSehs2F2WHiAssA1293D2+/bsfmfP+bYfYNkAWSDA0muAUEJCepmaTCbT+7ipu1f1896Pij2TycQjF1nS9Qf9xlLGmtfW8z7Xc3ddWgOEEEIIuST6Yl8AIYQQUgpQMAkhhJAZQMEkhBBCZgAFkxBCCJkBFExCCCFkBlAwCSGEkBlAwSSEEEJmAAWTEEIImQEUTEIIIWQGUDAJ... | <image><image_1>In H, the diameter is $18$, $LM = 12$, and $m \widehat {LM} = 84$. Find $HP$. Round to the nearest hundredth.
<image><image_2>Find x to the nearest tenth. Assume that segments that appear to be tangent are tangent. | 6.71
21.6 |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAb8AAAD7CAYAAAD6rZq8AAAvKUlEQVR4nO3de1yUZd4/8I8LrI6OICCOCioCIuJoHgBJKNwezawnMct8ctP0F7pPm+7mtphZrbm7+njY1i2ttrLMajVzPdbzlOWWFJoKgYdROSkog4gjgwyHgWXG+f0xMM7AMMzAHO7h/rxfL18vwBvmFmfmc1/f+7q+Vw+DwWAAERGRiPzM0ydARETkbgw/IiISHYYfERGJDsOPiIhEh+FHRESiw/AjIiLRYfgREZHoMPyIiEh0GH5ERCQ6... | <image><image_1>If $m \widehat{F E}=118, m \widehat{A B}=108$, $m \angle E G B=52,$ and $m \angle E F B=30$, find $m \widehat{C F}$
<image><image_2>If $c=5,$ find $a$ | 44
2.5 |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAANYAAAEvCAYAAAA5CT9LAAABRmlDQ1BJQ0MgUHJvZmlsZQAAKJFjYGASSSwoyGFhYGDIzSspCnJ3UoiIjFJgf8LAzCDOwM8gyyCcmFxc4BgQ4ANUwgCjUcG3awyMIPqyLsis6bce3FrtZzyDZVvGAdHJ7DMw1aMArpTU4mQg/QeI05MLikoYGBhTgGzl8pICELsDyBYpAjoKyJ4DYqdD2BtA7CQI+whYTUiQM5B9A8gWSM5IBJrB+ALI1klCEk9HYkPtBQFeF1cfH4VgVyNz... | <image><image_1>Find x.
<image><image_2>Find the length of $\widehat {AB}$. Round to the nearest hundredth. | 5
9.77 |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAXcAAAEVCAYAAAAb/KWvAAABRmlDQ1BJQ0MgUHJvZmlsZQAAKJFjYGASSSwoyGFhYGDIzSspCnJ3UoiIjFJgf8LAzCDAIMygwMCcmFxc4BgQ4ANUwgCjUcG3awyMIPqyLsgsvtePDO5HT+F5/1nLJXJfz25M9SiAKyW1OBlI/wHi9OSCohIGBsYUIFu5vKQAxO4AskWKgI4CsueA2OkQ9gYQOwnCPgJWExLkDGTfALIFkjMSgWYwvgCydZKQxNOR2FB7QYDXxdXHRyHY1cjc... | <image><image_1>In the figure, line $l$ is parallel to line $m$. Line $n$ intersects both $l$ and $m$. Which of the following lists includes all of the angles that are supplementary to $ ∠1 $?
<image><image_2>In the figure, $m∠3 = 43$. Find the measure of $\angle 11$. | angles 2,3, 6, and 7
43 |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAkgAAAGBCAYAAACdEU5OAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAACE+SURBVHhe7d1Niy3JnR5wfxMbvBvPSEY2GGzUlnc2SMh4YWMai1mMMTRa2XjRaDV402gz+AVJm/FisKTFeCkJxls1jNctxvuWvsDVJyj301TejvpXnlPnZOY5JyPy94OgX27dc2+9ZT0Z+UTE33oCAOAFAQkAoBCQAAAKAQkAoBCQAAAKAQkAoBCQ... | <image><image_1>If AB || DC, find x.
<image><image_2>Find the measure of $\angle 2$. | 115
33 |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAVoAAAF4CAYAAAAVNTFLAAABRmlDQ1BJQ0MgUHJvZmlsZQAAKJFjYGASSSwoyGFhYGDIzSspCnJ3UoiIjFJgf8LAzMDHIMQgw8CdmFxc4BgQ4ANUwgCjUcG3awyMIPqyLsisy79j76nNu7c/WdpE/GtOzxpM9SiAKyW1OBlI/wHi9OSCohIGBsYUIFu5vKQAxO4AskWKgI4CsueA2OkQ9gYQOwnCPgJWExLkDGTfALIFkjMSgWYwvgCydZKQxNOR2FB7QYDXxdXHRyHY1cjc... | <image><image_1>The diagram shows the layout of Elm, Plum, and Oak streets. Find the value of $x.$
<image><image_2>Find $y$. | 125
5 \sqrt { 5 } |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAR0AAAEZCAYAAACq+/FtAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAACK2SURBVHhe7Z3/bxTnncf7+/0RRDYgEjkQQqycksiVokDaXkO56s6lRYFDNDitSHLiIKWFIAHpFdIeRKld3blqTU912zNtzUlnrnGv2arZXE2bTev08AVDSIKvpoHg1qE2jlnv5/YzM4/98Xh2dmZ2vjwz835JjzCzu97Z2Xle8/l8nucZf4gAACBG... | <image><image_1>In $\odot P, m \angle M P L=65$ and $\overline{N P} \perp \overline{P L}$.
Find $m \widehat{N M}$
<image><image_2>Each pair of polygons is similar. Find y | 25
5 |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAnAAAAFzCAYAAAC+bzSQAADAnUlEQVR4nOz913tc+Xnoe35X5ZyrUMiRJAjmzGbsZuesblmSJUtO++wzc54zz8y5nv9hLmfmmZltb1uSbVmS1TknpmbOGSByFVLlnKvWXBQIokgwJ4Tf58KPxQbJIlC11rt+b5JkWZYRBEEQBEEQFgzFs34BgiAIgiAIwoMRAZwgCIIgCMICIwI4QRAEQRCEBUYEcIIgCIIgCAuMCOAEQRAEQRAWGBHACYIgCIIgLDAigBMEQRAEQVhgRAAn... | <image><image_1>Use parallelogram $JKLM$ to find $m \angle KJL$.
<image><image_2>Find the area of the figure. Round to the nearest tenth if necessary. | 30
63 |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAWYAAAEmCAYAAABRfjp6AAABRmlDQ1BJQ0MgUHJvZmlsZQAAKJFjYGASSSwoyGFhYGDIzSspCnJ3UoiIjFJgf8LAzCDGwMvAzWCZmFxc4BgQ4ANUwgCjUcG3awyMIPqyLsisayszrE7URYr5bTi99smnzY2Y6lEAV0pqcTKQ/gPE6ckFRSUMDIwpQLZyeUkBiN0BZIsUAR0FZM8BsdMh7A0gdhKEfQSsJiTIGci+AWQLJGckAs1gfAFk6yQhiacjsaH2ggCvi6uPj0Kwq5G5... | <image><image_1>Find the perimeter of the parallelogram. Round to the nearest tenth if necessary.
<image><image_2>Trapezoid $GHJK$ has an area of 75 square meters. Find the height. | 76
5 |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAQsAAACVCAYAAABPTt/VAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAABHPSURBVHhe7d37cxRVFgdw/pNYQVNaaFEBSktxS2WLEjeArgq1PrZY0cKtAt3itYu6qGhEVmDFWPgCQZfVxQV8IaKRZ0AQwcTlEbEIhkcgkIeYBwYi1tk+k/TMnc7p7ts9tyfdme8PnxLSd7ixp+c7954+mQz65cJZAsjFpYtn6deISfNCfiEsIGcI... | <image><image_1>Find x
<image><image_2>Find x. Round to the nearest tenth. | 58
30.2 |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAU8AAAD1CAYAAADQ63dVAAABRmlDQ1BJQ0MgUHJvZmlsZQAAKJFjYGASSSwoyGFhYGDIzSspCnJ3UoiIjFJgf8LAzCDGIM6gz2CQmFxc4BgQ4ANUwgCjUcG3awyMIPqyLsgs+VNVf877TN/6iLfO3WPuVBNM9SiAKyW1OBlI/wHi9OSCohIGBsYUIFu5vKQAxO4AskWKgI4CsueA2OkQ9gYQOwnCPgJWExLkDGTfALIFkjMSgWYwvgCydZKQxNOR2FB7QYDXxdXHRyHY1cjc... | <image><image_1>For the pair of similar figures, find the area of the green figure.
<image><image_2>In $\odot X, A B=30, C D=30,$ and $m \widehat{C Z}=40$
Find $m\widehat{C D}$ | 9
80 |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAksAAAEZCAYAAACHE2FjAAAhtElEQVR4nO3dfXBVdZ7n8S/djVW2DcQKAb1AwN0hAQJICQGSBmYZJAKzs61jY8PopHGCu25N0yXK0N1OGIpOFoVBcIYuZRdDY1ZWGtrBLmeMBmyrBcNDgKWRAMl1xpCQICYpb8IiVWbZ7B/0Odxzcu/Jueeeex7fr7848eb400oun/t7+JxBfX19fQIAAICEvuH2AAAAALyMsAQAAGCAsAQAAGCAsAQAAGCAsAQAAGCAsAQAAGCAsAQAAGCA... | <image><image_1>Quadrilateral EFGH is a rectangle. If FK = 32 feet, find EG.
<image><image_2>Find $x$. | 64
7 |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAYsAAAG9CAYAAADkw1o7AAABRmlDQ1BJQ0MgUHJvZmlsZQAAKJFjYGASSSwoyGFhYGDIzSspCnJ3UoiIjFJgf8LAzCDAIMygwMCcmFxc4BgQ4ANUwgCjUcG3awyMIPqyLsgsvtePDO5HT+F5/1nLJXJfz25M9SiAKyW1OBlI/wHi9OSCohIGBsYUIFu5vKQAxO4AskWKgI4CsueA2OkQ9gYQOwnCPgJWExLkDGTfALIFkjMSgWYwvgCydZKQxNOR2FB7QYDXxdXHRyHY1cjc... | <image><image_1>In the figure, $m \angle 1=4 p+15$, $m \angle 3=3 p-10$ and $m \angle 4=6 r+5 $. Find the value of $p$.
<image><image_2>Find x. | 25
\sqrt { 21 } |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAdUAAAHGCAYAAAAi+xHCAAAgAElEQVR4nOydBYAc1LWG/9nxWXd3j5GECAQI7u7BrY8KlYfT0lIoVqS0jwptaSkNSZAWDRokuMQDkXV39/HZd88d2dmN7W5mszOz53svDQnJMjty/3vsP4phARiGYRiGOWhCpvsBMAzDMEywwKLKMAzDMD6CRZVhGIZhfASLKsMwDMP4CBZVhmEYhvERLKoMwzAM4yNYVBmGYRjGR7CoMgzDMIyPYFFlGIZhGB/BosowDMMwPoJFlWEYhmF8... | <image><image_1>Find $BC$.
<image><image_2>Find x. | 13
24 \sqrt { 3 } |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAYkAAAD2CAYAAAAj3nsdAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAA/ISURBVHhe7d29j2RVesBhAqcWkhMHDkAicsJIJI74+ANAI8cj4XyEvJITayBA1iZjhIwTPiI2AkISwFiyBCtGMloJrRjkYGWQPWjlYGXDaAMcELT99tZp3q6pc7qqu27VPec+j3TETk11d9W51edX96NmHzoBgAqRAKBKJACoEgkAqkQCgCqRAKBK... | <image><image_1>If $ZP = 4x - 9$ and $PY = 2x + 5$, find $ZX$.
<image><image_2>Find y | 38
6 \sqrt { 3 } |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAOcAAAF8CAYAAAA0IqwUAAABRGlDQ1BJQ0MgUHJvZmlsZQAAKJFjYGASSSwoyGFhYGDIzSspCnJ3UoiIjFJgf8LAzCAOhFwMMonJxQWOAQE+QCUMMBoVfLvGwAiiL+uCzEqVMn959v6/xLuzzs/X2pt8BlM9CuBKSS1OBtJ/gDg9uaCohIGBMQXIVi4vKQCxO4BskSKgo4DsOSB2OoS9AcROgrCPgNWEBDkD2TeAbIHkjESgGYwvgGydJCTxdCQ21F4Q4HVx9fFRCHY1Mje0... | <image><image_1>Find the measure of $∠T$ to the nearest tenth.
<image><image_2>Find x to the nearest tenth. Assume that segments that appear to be tangent are tangent. | 21.8
7.2 |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAesAAAHBCAYAAABJxJPxAAAgAElEQVR4nOy9B2Cb1332+2ATIAAOEOAUlyiKGtTe1qTkIbtesmMnHvGMnfE1uW26+/Xe3va7ve3N15E2SeM48czwtuN4yLKWtSVKokSJEiVS4iY2QZAgiY17zgFAUVvcIPn/xW9AUiT4Enjf85z/lkQYIAiCIAgiYZGO9wkQBEEQBHFjSKwJgiAIIsEZsliHw+GRPA+CIAiCIK7DkMSah7lDoRAo3E0QBEEQo49kKAlm/EckEslonA9BEARB... | <image><image_1>$\overline{AB} \cong \overline{DF}$. Find $x$.
<image><image_2>Find $m \angle WYZ$. | 2
23 |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAQgAAADSCAYAAAC2JF4CAAABRmlDQ1BJQ0MgUHJvZmlsZQAAKJFjYGASSSwoyGFhYGDIzSspCnJ3UoiIjFJgf8LAzCDGIMRgyKCfmFxc4BgQ4ANUwgCjUcG3awyMIPqyLsisB/O42vdrVBiX2l66POt2/ANM9SiAKyW1OBlI/wHi9OSCohIGBsYUIFu5vKQAxO4AskWKgI4CsueA2OkQ9gYQOwnCPgJWExLkDGTfALIFkjMSgWYwvgCydZKQxNOR2FB7QYDXxdXHRyHY1cjc... | <image><image_1>Find the area of the shaded region.
<image><image_2>Find x | 22.1
2 |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAUIAAAEICAYAAAAqbv2WAAAyrUlEQVR4nO3de0BT590H8C8lFIIYBMSIhIuAiBgVFNAKFtfXW29qtep0ra0rdavDbq7VOVtnXWdfq2udl7ZrS6vVvVrrvGC7VqttpQWroqASEREQMIgYAUEgMBLz/hFPSELIhZxcz+/zV7AnyVNIvue5nd/xUKlUKhBCCIc94OgGEEKIo1EQEkI4j4KQEMJ5FISEEM6jICSEcB4FISGE8ygICSGcR0FICOE8CkJCCOdREBJCOI+CkBDCeRSE... | <image><image_1>In $\odot O, \overline{E C}$ and $\overline{A B}$ are diameters, and $\angle B O D \cong \angle D O E \cong \angle E O F \cong \angle F O A$
Find $m\widehat{A D}$
<image><image_2>Find $x$ if $AE=3, AB=2$, $BC=6,$ and $ED=2x-3$ | 135
6 |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAOMAAAEJCAYAAABmJpAcAAAcgklEQVR4nO2deXxU5b3/38lkQgYSE8MA2SCBQAiLkEAAWa3Iq4oWLaBtfve6XL3Xtvqr0iv6q0sttffagvXW5V57VaqI2ltL1boUF35qRRGUxVDZAiGQjSwQQvZtMjP3j2GSASYzZ5JZzvJ9/5OT5Dk5z0zOe57l85xzono6q50IghBxoiNdAUEQXIiMgqASREZBUAkioyCoBJFREFSCyCgIKkFkFASVIDIKgkoQGQVBJYiMgqASREZBUAki... | <image><image_1>Find $A E$ if $A B=12, A C=16,$ and $E D=5$
<image><image_2>Find $x$ in the given parallelogram | 15
38 |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAUsAAAC2CAYAAABQzK/tAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAABLZSURBVHhe7d2PbxT3ncbx/idEmFgNIiJArKIeMUqE0gYRX4JaRA+dQIUEUh3NXURQJQgS5E46kO6CeoB0vejsKOXSgE6QXkGCq3CuENXKxSQmggZHQGsSqzWNKXGNzxj2c/PY+7W/TGZ3Z9f7Y2b2/ZJGlX+lwM48+/nOMzP+mgEASiIsASAGwhIA... | <image><image_1>Find x
<image><image_2>Find the area of the figure. Round to the nearest tenth if necessary. | 115
129.9 |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAZ8AAAGmCAYAAACjl4nxAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAC1/SURBVHhe7d1RqC3Xfd/x+1AMaRMCDfShaSqD2qckVnCeGiNVTUmaFAlBQxOcC0ofEuLKhoJd4974IXGdwEW0iBAqC4rdQmvrQYZAkEQd2ritbrFT0oZcRYGQhiCphFCS+KoPyUMfdu/vaK+r//6fNTNrZtasWWvW9wML6Zyz97ln73NmfrP+6z8z... | <image><image_1>Find $a$ in the given parallelogram
<image><image_2>Find $m\angle B$ | 9
120 |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAY4AAAGzCAYAAAA44PAPAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAACCXSURBVHhe7d1Pqy1VesfxfiONgm9BLuQlXHwDFwcZKg56EpQ7caLgINAiOAmItEOxceBExBAQWkTSdCCKg05oUKF7EgLeQEaZnNRvu/f1qees+rOqVtX69/3AM7jn7LPP3lXn1q9W1VrP/tUdAAARCA4AQBSCAwAQheAAAEQhOAAAUQgOAEAUggMA... | <image><image_1>Find GH in the kite
<image><image_2>Find the value of the variable $x$ in the figure. | \sqrt { 369 }
125 |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAfQAAAEXCAYAAABbBramAAABRmlDQ1BJQ0MgUHJvZmlsZQAAKJFjYGASSSwoyGFhYGDIzSspCnJ3UoiIjFJgf8LAzCDAIMygwMCcmFxc4BgQ4ANUwgCjUcG3awyMIPqyLsgsvtePDO5HT+F5/1nLJXJfz25M9SiAKyW1OBlI/wHi9OSCohIGBsYUIFu5vKQAxO4AskWKgI4CsueA2OkQ9gYQOwnCPgJWExLkDGTfALIFkjMSgWYwvgCydZKQxNOR2FB7QYDXxdXHRyHY1cjc... | <image><image_1>Refer to the figure at the right. Find the value of $m ∠FCE$ if $ p \parallel q $.
<image><image_2>What is the measure of $\angle B$ if $m \angle A=10 ?$ | 105
30 |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAVYAAADRCAYAAACXbZpXAAABRWlDQ1BJQ0MgUHJvZmlsZQAAeJxjYGASSSwoyGFhYGDIzSspCnJ3UoiIjFJgf8LAzCDJwMPAyGCWmFxc4BgQ4ANUwgCjUcG3a0B1QHBZF2TWrUbLwmfhj38ssohM0zVmMsBUjwK4UlKLk4H0HyBOTy4oKmFgYEwBspXLSwpA7A4gW6QI6Cggew6InQ5hbwCxkyDsI2A1IUHOQPYNIFsgOSMRaAbjCyBbJwlJPB2JDbUXBHhdXH18FIJdjcwN... | <image><image_1>Express the ratio of $\cos N$ as a decimal to the nearest hundredth.
<image><image_2>Find $m \angle R$ | 0.38
29.1 |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAv0AAAFyCAYAAABmyGWEAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAAEnQAABJ0Ad5mH3gAAKCNSURBVHhe7d0HfJT1/QfwT9Zl70UgIQTIYDgAlaEgLoYKDtTa9t/WVbfWah3Vam3VWq2r7lG7h3sAKiC42CgiCmQSsoDsPS6X5PL/fZ+7e+4uJpBAxo3P+9VUEg5I7u75Pd/n93x+359PtwIiIiIiIvJYvtb/EhERERGRh2LRT0RERETk4Vj0ExER... | <image><image_1>Find $x$.
<image><image_2>Find the area of the figure. Round to the nearest tenth. | 8
50.2 |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAP0AAAEdCAYAAADHBmHKAAABRmlDQ1BJQ0MgUHJvZmlsZQAAeJxjYGASSSwoyGFhYGDIzSspCnJ3UoiIjFJgf8LAzCDOwM8gyyCcmFxc4BgQ4ANUwgCjUcG3awyMIPqyLsis6bce3FrtZzyDZVvGAdHJ7DMw1aMArpTU4mQg/QeI05MLikoYGBhTgGzl8pICELsDyBYpAjoKyJ4DYqdD2BtA7CQI+whYTUiQM5B9A8gWSM5IBJrB+ALI1klCEk9HYkPtBQFeF1cfH4VgVyNz... | <image><image_1>Find y.
<image><image_2>Find the area of the shaded sector. Round to the nearest tenth. | 21 \sqrt { 3 }
182.6 |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAN8AAAFDCAYAAAC6KtugAAABRGlDQ1BJQ0MgUHJvZmlsZQAAKJFjYGASSSwoyGFhYGDIzSspCnJ3UoiIjFJgf8LAzCAEFGRmEEhMLi5wDAjwAfIYYDQq+HaNgRFEX9YFmXXT7Mim4rkXSq/kTk22YHhQjKkeBXClpBYnA+k/QJyeXFBUwsDAmAJkK5eXFIDYHUC2SBHQUUD2HBA7HcLeAGInQdhHwGpCgpyB7BtAtkByRiLQDMYXQLZOEpJ4OhIbai8I8Lq4+vgoBLsamRta... | <image><image_1>$\triangle K L N$ and $\triangle L M N$ are isosceles and $m \angle J K N=130$. Find the measure of $\angle J$.
<image><image_2>Find x. | 106
12 |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAATEAAADWCAYAAAC5U7XmAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAABGrSURBVHhe7d3Nq51XFcfx/gcOOyopdOBAaKADZ639A1ryBwTqPBQEJxI7KNRJCIJO+jLSiW2GnaTFgaC2F5VCERMciIokioKgXhzowMGxv/Ss25V9n/O8nPPs/ey19/cDmzbJuel92ee39lpn39sndgAQGCEGIDRCDEBohBiA0AgxAKERYgBCI8QA... | <image><image_1>$ABCD$ is a rhombus. If $PB = 12$, $AB = 15$, and $m \angle ABD = 24$, Find $m\angle BDA$
<image><image_2>Find $y$. | 24
12 |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAkcAAAFjCAYAAAA3lq9KAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAACRYSURBVHhe7d09qDTZmR/wBadeNnHkRALlEijflRInRmJyC7Q4FYIBs2BmhVnDJkIYJtIHGLSJV3I2iVZsYDM7aAKzIAtJVjB4lkWD2ECw40GBN3Bwzf/VPa+e90xVdXV3VXdV1+8Hh5n33rrd9/ZHnX8/56N+7wkAgJeEIwCAQjgCACiEIwCAQjgC... | <image><image_1>Find the value of $x$ in each diagram
<image><image_2>Find $m \angle RST$. | 68
55 |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAARwAAACxCAYAAAAWAQJkAAABRmlDQ1BJQ0MgUHJvZmlsZQAAKJFjYGASSSwoyGFhYGDIzSspCnJ3UoiIjFJgf8LAzMDHIMQgw8CdmFxc4BgQ4ANUwgCjUcG3awyMIPqyLsisy79j76nNu7c/WdpE/GtOzxpM9SiAKyW1OBlI/wHi9OSCohIGBsYUIFu5vKQAxO4AskWKgI4CsueA2OkQ9gYQOwnCPgJWExLkDGTfALIFkjMSgWYwvgCydZKQxNOR2FB7QYDXxdXHRyHY1cjc... | <image><image_1>$∠6$ and $∠8$ are complementary, $m∠8 = 47$. Find the measure of $\angle 7$.
<image><image_2>Find the measure of $m\angle 1$. Assume that segments that appear
tangent are tangent. | 90
129 |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAVYAAACVCAYAAAADpNItAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAABbeSURBVHhe7d3/UxRnngfw/TO27he3QCmTMitKKC1joJIiVuSisbiVuEdFTKHi7S2SykH2KmK2NMlGvBWsBLIJ6wa8LGYXNovmhJQk66RKUsGsGMHDiyQhCegQcR3FCY4w0O/rT9MNLcxX6Bmmm/er6ilNM1SZZ55+99PP8/TTPwIREVmKwUpEZDEG... | <image><image_1>Let $\overline{G H}$ be the median of $R S B A .$ Find $G H$
<image><image_2>Use parallelogram PQRS to find $QP$ | 62
5 |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAfcAAAHbCAYAAADWG9NqAAAgAElEQVR4nOydB2Db1bXGP9mSJVny3jN2bMcjzt6LhAQSdlllQynQllVoKa900kVpoXRAKaUto+xd9ggjgyyytxOPOPG2vIeGNWy/e66G5ZA4ji0v+fzeU02GFVn/v+53z7nnfEfRLQDDMAzDMH5DwEi/AIZhGIZhfAuLO8MwDMP4GSzuDMMwDONnsLgzDMMwjJ/B4s4wDMMwfgaLO8MwDMP4GSzuDMMwDONnsLgzDMMwjJ/B4s4wDMMwfgaL... | <image><image_1>Quadrilateral $WXYZ$ is inscribed in $\odot V$. Find $m \angle X$.
<image><image_2>Find the height of the parallelogram given its area with 2000 square units. | 120
40 |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAm0AAAF9CAYAAABWNV+4AAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAADb/SURBVHhe7d13dFVV2sfxqPOOYxlHeu+9KAii0m0zNpqgoiJiQ5GOSEeld1QsSBMEEaUooCKQSu+9hE4oCSUNEtILz3v2vhsQpSRwc3LPzfez1l445zm580/uzu/ss4uPAAAAwOMR2gAAAByA0AYAAOAAhDYAAAAHILQBAAA4AKENAADAAQhtAAAA... | <image><image_1>Find $m \angle A$ of quadrilateral ABCD
<image><image_2>Find y | 135
10 |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAWkAAADbCAYAAACvDmCEAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAABTZSURBVHhe7d2PcxRlnsdx/xMtIhRu6R0/pI7iXKi74jjdU9ajdjksq048tHC9Q/fcwFUpxZ3uXq2hXPSU7F5hCbE0W7tBN7hVYU9ZjCusF26NAgoncY0uIPGCBGIWQgiZ783T6SeZPOnJdM9Mzzz9PO9X1VOQnh+Zycx8pufpT/dcIwAAaxHSAGAx... | <image><image_1>Find the measure of the altitude drawn to the hypotenuse.
<image><image_2>Find the area of the shaded region. Round to the nearest tenth. | 4 \sqrt { 3 }
157.1 |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAYcAAADBCAYAAAAkaHy7AAABRmlDQ1BJQ0MgUHJvZmlsZQAAKJFjYGASSSwoyGFhYGDIzSspCnJ3UoiIjFJgf8LAzCDOIMagxMCUmFxc4BgQ4ANUwgCjUcG3awyMIPqyLsgshq8p1i5tGxpuH1q24uOJ7/cw1aMArpTU4mQg/QeI05MLikoYGBhTgGzl8pICELsDyBYpAjoKyJ4DYqdD2BtA7CQI+whYTUiQM5B9A8gWSM5IBJrB+ALI1klCEk9HYkPtBQFeF1cfH4VgVyNz... | <image><image_1>Find x. Round to the nearest tenth.
<image><image_2>Find $y$ in each figure. | 30.7
6 |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAfAAAAHTCAYAAADYlEp+AADXlklEQVR4nOzddXic15n4/e8wz2ikEY5YJpmZKcycNEnDabhpUtpu29399d3tdrdLbdMGmzRpmJkTx07MzLZkW7LFNJKGGZ73j5EFjkFSbGskn891pUltwUgz89zPOecGmSRJEoIgCIIgDCvyoX4AgiAIgiAMnAjggiAIgjAMiQAuCIIgCMOQCOCCIAiCMAyJAC4IgiAIw5AI4IIgCIIwDIkALgiCIAjDkAjggiAIgjAMiQAuCIIgCMOQCOCC... | <image><image_1>Find $m \angle S$.
<image><image_2>In the figure, $m∠3 = 110$ and $m ∠ 12 = 55$. Find the measure of $∠13$. | 34
55 |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAQcAAAEWCAYAAABrIVKZAAABRmlDQ1BJQ0MgUHJvZmlsZQAAKJFjYGASSSwoyGFhYGDIzSspCnJ3UoiIjFJgf8LAzCDOIMxgxKCQmFxc4BgQ4ANUwgCjUcG3awyMIPqyLsisy9KZZ1r+/9V1aWsTOvyc7xmmehTAlZJanAyk/wBxenJBUQkDA2MKkK1cXlIAYncA2SJFQEcB2XNA7HQIewOInQRhHwGrCQlyBrJvANkCyRmJQDMYXwDZOklI4ulIbKi9IMDr4urjoxDsamRu... | <image><image_1>Find x.
<image><image_2>Quadrilateral EFGH is a rectangle. If $m \angle HGE = 13$, find $m\angle FGE$. | 3 \sqrt { 35 }
77 |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAj4AAAF7CAYAAADST4HuAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAACbESURBVHhe7d3Nqi3XtR9wv0iwwa9gBHqEg19AuJGmjRvuBBt1bscGNwQxBncCxthN4+BGOkJIBAzXGKNwBbFRIwkB23DTEQEpkFY6Oxo6u6R5xpm1VtWqWZ/z94PB0f5YtT+q0PzvWXPM+toTAEAnBB8AoBuCDwDQDcEHAOiG4AMAdEPwAQC6IfgA... | <image><image_1>Find x in the parallelogram
<image><image_2>Find the side length in isosceles triangle $DEF$. | 37
11 |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAbAAAAGrCAYAAAChX8JyAAAgAElEQVR4nOy9d3jb15nv+UUvBIlCgJ0iKVGiRPViNcuSW9zi3hKXxE7PncnM3czOvbv/7T5797m7e3dn7p1MTSaJ45bEjnuNuyVLsprVu8TeCwgQvWPPewBQlKxCUqRAAO/nMcwiEPwRODjf83ZFUgCGYRiGyTGU2b4AhmEYhpkKLGAMwzBMTsICxjAMw+QkLGAMwzBMTsICxjAMw+QkLGAMwzBMTsICxjAMw+QkLGAMwzBMTsICxjAMw+Qk... | <image><image_1>Find the length of $\widehat {JK}$. Round to the nearest hundredth.
<image><image_2>Use parallelogram to find $b$ | 13.74
11 |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAkkAAAF8CAYAAADb3y+3AAAxK0lEQVR4nO3deXwU9eH/8XfchCOEQNCAIeEIJOFIgoRThSpa8a5UarWiqAit+i3aYqs9rN/a2tPWo4r6U7Fo9evFtyhatVq+LSqHcgUh4QokGAIBAoQjEGOy7O+PkL2YTfaY3Z3dfT0fjz4endndyQjMziszn5lJcjgcDgEAAMDDadFeAQAAACsikgAAAAwQSQAAAAaIJAAAAANEEgAAgAEiCQAAwACRBAAAYIBIAgAAMEAkAQAAGCCSAAAA... | <image><image_1>If PR || KL, KN = 9, LN = 16, PM = 2 KP, find MN
<image><image_2>Find $x$. Round to the nearest tenth. | 12
14.1 |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAVAAAADQCAYAAABRLzm1AAABRmlDQ1BJQ0MgUHJvZmlsZQAAKJFjYGASSSwoyGFhYGDIzSspCnJ3UoiIjFJgf8LAzCDGIMrAzyCemFxc4BgQ4ANUwgCjUcG3awyMIPqyLsisD4+2Fz1M7jyRZ5HacOf0wcmY6lEAV0pqcTKQ/gPE6ckFRSUMDIwpQLZyeUkBiN0BZIsUAR0FZM8BsdMh7A0gdhKEfQSsJiTIGci+AWQLJGckAs1gfAFk6yQhiacjsaH2ggCvi6uPj0Kwq5G5... | <image><image_1>Find the area of the rhombus.
<image><image_2>Find TX if $E X=24$ and $D E=7$ | 132
32 |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAtgAAAHKCAYAAAA5JTwIAAAgAElEQVR4nOzdBYCc1bk+8Gfc1t3d4h4IEIIFD+4QqFODAkVbaEvbf3uhQAVob29baHGnaBIIHoV4djfrWXedHbf9f+fMrCRsfJPsJs/v3mmWldnZmfm+857zved9VQMKEBERERHRmFAf7QdARERERHQsYYBNRERERDSGGGATEREREY0hBthERERERGOIATYRERER0RhigE1ERERENIYYYBMRERERjSEG2EREREREY4gBNhERERHRGGKATURE... | <image><image_1>Find $m \widehat {LP}$.
<image><image_2>Express the ratio of $\sin N$ as a decimal to the nearest hundredth. | 150
0.92 |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAATAAAAD9CAYAAAA7+istAAABRGlDQ1BJQ0MgUHJvZmlsZQAAKJFjYGASSSwoyGFhYGDIzSspCnJ3UoiIjFJgf8LAzCDJwA2EoonJxQWOAQE+QCUMMBoVfLvGwAiiL+uCzPKNvnxTJODwXuf8/uedhyZZYqpHAVwpqcXJQPoPEKcnFxSVMDAwpgDZyuUlBSB2B5AtUgR0FJA9B8ROh7A3gNhJEPYRsJqQIGcg+waQLZCckQg0g/EFkK2ThCSejsSG2gsCvC6uPj4Kwa5G5oaW... | <image><image_1>Find x.
<image><image_2>Find the area of the figure. Round to the nearest hundredth, if necessary. | 1
4.8 |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAlsAAAHwCAYAAACR9qrBAAAgAElEQVR4nOzdB5icZaE2/vt9p+xs732zfTe9Nwg1AUkAAQWRJgqIVI8ej56jx/P9v+v7rlNsnx490gRBRbBQpZNCgEh679ma7b336f/3eWZ2dzbJliQ7O+3+eY1JhiS8CTsz9/uU+1GcGhARERGRV6i+vgAiIiKiYMawRURERORFDFtEREREXsSwRURERORFDFtEREREXsSwRURERORFDFtEREREXsSwRURERORFDFtEREREXsSwRURERORF... | <image><image_1>Find $x$.
<image><image_2>Use parallelogram ABCD to find $m\angle ADC$ | 3.5
128 |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAi8AAAD5CAYAAADvLNVfAAABRmlDQ1BJQ0MgUHJvZmlsZQAAKJFjYGASSSwoyGFhYGDIzSspCnJ3UoiIjFJgf8LAzCDEwMVgyqCVmFxc4BgQ4ANUwgCjUcG3awyMIPqyLsis3Utj/vW8f8nssnDSwp/ruCwx1aMArpTU4mQg/QeI05MLikoYGBhTgGzl8pICELsDyBYpAjoKyJ4DYqdD2BtA7CQI+whYTUiQM5B9A8gWSM5IBJrB+ALI1klCEk9HYkPtBQFeF1cfH4VgVyNz... | <image><image_1>Find the measure of $\angle 3$ if $\overline{A B} \perp \overline{B C}$.
<image><image_2>In $\triangle DEF, m \angle E=108, m \angle F=26$, and $f=20$, Find $d$ to the nearest whole number. | 76
33 |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAATEAAAD4CAYAAACE9dGgAAA+nklEQVR4nO2deVhU5fuHbwJUEBdQRAMBBRQUVwQXMK3cy72sXPOrlZpmZpZpZVaWa9ZPs0XLJdPURG0xNSstcAFFcRdQUSFCBBSBAWGc3x/jjAMM+yznzLz3dXld4Jwz83DmnM953+c8z+e1UalUKgQCgUCmPGTuAAQCgaA6CBETCASyRoiYQCCQNULEBAKBrBEiJhAIZI0QMYFAIGuEiAkEAlkjREwgEMgaIWICgUDWCBETCASyRoiYQCCQ... | <image><image_1>Find $y$ so that each quadrilateral is a parallelogram.
<image><image_2>Find $m \angle 4$. | 4
33 |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAdgAAAFDCAYAAACZeB8ZAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAACCGSURBVHhe7d3/c1T3vd/x/if2IGAwQy5fZNUJdqBmMAYaU8y1NZ4wATsYK7gGMi7+MkH2DNAfkMdX+CbId6J0Ruq1lduA26Vt4DYiYznXairueKmhRY0Vg2MgUhBj2aABgST2VX3EOdJHh5W0X87n7Dm7z8fM+SHa1eJIu/vU++znnPMvBAAAQkdg... | <image><image_1>Find $cos C$
<image><image_2>In rhombus $A B C D, m \angle D A B=2, m \angle A D C$ and $C B=6$. Find $m \angle A C D$ | \frac { 4 } { 5 }
60 |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAYkAAAELCAYAAAAspXpuAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAACQJSURBVHhe7d2Pc1TXeTfw/CfySEZje3D5FQaPjWHMEFIzDvHLGJWEsSEFjJsGcF3g9QwyGSBpgEmBN0ZuXpJacls5qXAs3Bhaqy7rieWOcJGN4IUGEWMH2VINRlgoQugH+3332b1HOhF7d+/u3h/n3Pv9zNxJvCzYrO7e7z3nec65XwEREZELhgQR... | <image><image_1>Find AB
<image><image_2>Find $x$ in the figure. | 10
14 |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAUMAAAD9CAYAAAAmhBW2AAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAB9FSURBVHhe7Z2Nc1T1ucf9T3QSZNTB8taMHS+FkaHcyihVBlMsI7SlEqa3Qq9DvE55uUNoKzC3hOGlddJ7TSyz6iS0sa3Qa65lnRJngs1qQZOWYCMlGiRIFNK8mJd97nnOnl/ycHJ295yz532/n5nfiJvdZPfsOZ/f8/xennMbAQAAIMgQAAA0IEMA... | <image><image_1>Circle $O$ has a radius of 13 inches. Radius $\overline{O B}$ is perpendicular to chord $\overline{C D}$ which is 24 inches long.
If $m \widehat{C D}=134,$ find $m \widehat{C B}$
<image><image_2>In $\odot M$, $FL=24,HJ=48$, and $m \widehat {HP}=65$. Find $FG$. | 67
48 |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAy0AAAH5CAYAAACMINEWAAAgAElEQVR4nOzd91ccd+Lu+ac6B2ianBEIBRSQjLJkJSvalpOSJTmMJ97Zvbv33u/9Zc/+B7tnw7lnx2k8HifJCrblLCclK+cACiggiSRypmk6d21VNSBAIAkJ6G54Xp6eGaDpLhCm661PKEGUgIiIiIiIKESpgn0ARERERERED8JoISIiIiKikMZoISIiIiKikMZoISIiIiKikMZoISIiIiKikMZoISIiIiKikMZoISIiIiKikMZoISIiIiKi... | <image><image_1>Cut four congruent triangles off the corners of a rectangle to make an octagon. What is the area of the octagon?
<image><image_2>Find $m\angle A$ | 528
60 |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAXcAAAD7CAYAAACRxdTpAAA9OElEQVR4nO3deVyU5f7/8RcCKoQbqwiyCSiKmihqrlRq5qlIzUpLs5PVaV/157FFrWPnpG3fk2mdNJfUFnPNVs20xAXXFBc2WQQR2WSRRRjm98c4w6DsMsw993yej0ePB8nijTPznuu+7ut63zZarVaLEEIIVWll7gMQQgjR/CTchRBChSTchRBChSTchRBChSTchRBChSTchRBChSTchRBChSTchRBChSTchRBChSTchRBChSTchRBChSTc... | <image><image_1>Use parallelogram JKLM to find $m \angle KJL$ if $J K=2 b+3$ and $J M=3 a$.
<image><image_2>Find x. | 30
\frac { 17 } { 2 } \sqrt { 3 } |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAl4AAAGICAYAAACQru4pAAAgAElEQVR4nOzdd3Cc54Em+KcDOqMbOWcQJEACIEEQIKhsS7IkS1aWbGXb8rhmr2Zm72b/uK3bq7q7ur+2autm9+pqquwZ24pWsBWtZAVLlEQxIQdm5JwbnXPf977dYBLB2GiCxPOraokggSbYaOB7+g3Pq4oqQERERESrTn21PwEiIiKi9YLBi4iIiChJGLyIiIiIkoTBi4iIiChJGLyIiIiIkoTBi4iIiChJGLyIiIiIkoTBi4iIiChJGLyI... | <image><image_1>Find $XZ$.
<image><image_2>Find $XW$. | 34
12 |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAUcAAAEICAYAAADMRzbSAAAKuWlDQ1BJQ0MgUHJvZmlsZQAASImVlgdUU1kax+97L52EFnoNvSNFIICU0ANI76ISkkBCCTEhqFiwMDiCY0FEBJQRUSkKjkqRsSKKbVBs2AdERNRxsCAqKvuAJczsnt09+51zc3/58t2vvPNuzh8A8leWUJgBywOQKcgWRfh70eLiE2j4ZwABcoAKcADLYouFjLCwYIDazP53+3gXQJP7LavJXP/++381BQ5XzAYACkM5mSNmZ6J8HF3P2EJR... | <image><image_1>Find x so that $GJ \parallel FK$. $G H=x+3.5, H J=x-8.5, F H=21, H K=7$.
<image><image_2>In $\odot P, m \angle M P L=65$ and $\overline{N P} \perp \overline{P L}$.
Find $m \widehat{N J K}$ | 14.5
155 |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAXMAAAFMCAYAAAA5llzqAAAgAElEQVR4nO2dB3xV5fnHf5mE7M2GDEhCgABhDxmCAgIOcFRr3dZ/h7XTyqYqo7XL1lptHbi1ooAIKDjYEPbKDmEmhOy9SML/PG/uOdybPW7uPeP5fnqbQYRzcs/5nud93ud9XofrEmAYhmE0jaO9D4BhGIbpPCxzhmEYHcAyZxiG0QEsc4ZhGB3AMmcYhtEBLHOGYRgdwDJnGIbRASxzhmEYHcAyZxiG0QEsc4ZhGB3AMmcYhtEBLHOGYRgd... | <image><image_1>A square is inscribed in a circle having a radius of $6$ inches. Find the length of each side of the square.
<image><image_2>One diagonal of a rhombus is twice as long as the other diagonal. If the area of the rhombus is 169 square millimeters, what are the lengths of the diagonals? | 6 \sqrt 2
26 |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAATAAAAC5CAYAAACvM2NXAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAA+HSURBVHhe7d2Bb5T3fcfx/CeObGIVROQEgoKixNEqRAsCj6HWo0FrUdcNNomQRgZpCyAZNhWiBqwOIy2r5ks3ay1N5bQKlsIiTBvaOV1IMREMHMXtTOO2TmPiuuDYxvfp8z0/j313fs53ts93z+953i/pJ+G7xwjd3fPh9/s+v+d7DwgAHEWAAXAW... | <image><image_1>Find x
<image><image_2>If $AB=12,AC=16$, and $ED=5$, find $AE$. | 9
15 |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAigAAAFNCAYAAAAq3JTxAAABRmlDQ1BJQ0MgUHJvZmlsZQAAKJFjYGASSSwoyGFhYGDIzSspCnJ3UoiIjFJgf8LAzMDHIMQgw8CdmFxc4BgQ4ANUwgCjUcG3awyMIPqyLsisy79j76nNu7c/WdpE/GtOzxpM9SiAKyW1OBlI/wHi9OSCohIGBsYUIFu5vKQAxO4AskWKgI4CsueA2OkQ9gYQOwnCPgJWExLkDGTfALIFkjMSgWYwvgCydZKQxNOR2FB7QYDXxdXHRyHY1cjc... | <image><image_1>Find $x$ so that $\overline{BE}$ and $\overline{AD}$ are perpendicular.
<image><image_2>Find DE | 10
9 |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAQ8AAAEACAYAAACtefPrAAABRmlDQ1BJQ0MgUHJvZmlsZQAAKJFjYGASSSwoyGFhYGDIzSspCnJ3UoiIjFJgf8LAzCDGIM6gz2CQmFxc4BgQ4ANUwgCjUcG3awyMIPqyLsgs+VNVf877TN/6iLfO3WPuVBNM9SiAKyW1OBlI/wHi9OSCohIGBsYUIFu5vKQAxO4AskWKgI4CsueA2OkQ9gYQOwnCPgJWExLkDGTfALIFkjMSgWYwvgCydZKQxNOR2FB7QYDXxdXHRyHY1cjc... | <image><image_1>Find the area of the shaded region formed by the circle and regular polygon. Round to the nearest tenth.
<image><image_2>In the figure, $m ∠ 12 = 64$. Find the measure of $ \angle 7$. | 76.4
64 |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAZ0AAAF3CAYAAAB+AJZGAAAgAElEQVR4nOydB1hbV7bv/+oVIXrHYGyDC+7dOM1JHDu9NyeTXiaZcvv3bpu5d96U9707d+6bSSZ10vtkkniSOHF6XHDv2KZ3hOgC1Os7+0g6EhgwxhhU1u+LYoqQZc4++7/X3mv9l8jHAYIgCIKYAsTT/QYIgiCI+IFEhyAIgpgySHQIgiCIKYNEhyAIgpgySHQIgiCIKYNEhyAIgpgySHQIgiCIKYNEhyAIgpgySHQIgiCIKYNEhyAIgpgy... | <image><image_1>Find $BC$.
<image><image_2>Find $m \angle 1$. | 9
37.5 |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAQsAAAGcCAYAAADONoWpAAABRWlDQ1BJQ0MgUHJvZmlsZQAAKJFjYGASSSwoyGFhYGDIzSspCnJ3UoiIjFJgf8LAzCDJwMPAyGCWmFxc4BgQ4ANUwgCjUcG3a0B1QHBZF2TWrUbLwmfhj38ssohM0zVmMsBUjwK4UlKLk4H0HyBOTy4oKmFgYEwBspXLSwpA7A4gW6QI6Cggew6InQ5hbwCxkyDsI2A1IUHOQPYNIFsgOSMRaAbjCyBbJwlJPB2JDbUXBHhdXH18FIJdjcwN... | <image><image_1>Express the ratio of $\sin P$ as a decimal to the nearest hundredth.
<image><image_2>Find $x$. $A=357$ in$^2$. | 0.88
21 |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAhgAAAD6CAYAAADjlz6wAAABRmlDQ1BJQ0MgUHJvZmlsZQAAKJFjYGASSSwoyGFhYGDIzSspCnJ3UoiIjFJgf8LAzMDHIMQgw8CdmFxc4BgQ4ANUwgCjUcG3awyMIPqyLsisy79j76nNu7c/WdpE/GtOzxpM9SiAKyW1OBlI/wHi9OSCohIGBsYUIFu5vKQAxO4AskWKgI4CsueA2OkQ9gYQOwnCPgJWExLkDGTfALIFkjMSgWYwvgCydZKQxNOR2FB7QYDXxdXHRyHY1cjc... | <image><image_1>Find $x$ so that $a ∥ b$.
<image><image_2>$\overline{GJ}$ is a diameter of $\odot K$. Find $m \widehat {GLJ}$. | 14
180 |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAXcAAADaCAYAAABdNQJ6AAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAABn0SURBVHhe7Z3/c1zVdcDzZ+Q3GAt7gDG1HeEJ46Rk8DgQPLHjpkXjCRMHClhpBpwMYxNaHDq2k4lFiZUJOCkqRWYS0cQOFWmxU6shSvDS2ARBhWsVFMdQy5ZABGFb6AuWtKc6b9+zr6/f7r79Jr179/OZOYO12l1We9/7vPPOPe++jwkAAHgHcgcA... | <image><image_1>Find $C F$ if $\overline{B F}$ bisects $\angle A B C$ and $\overline{A C} \| \overline{E D}, B A=6, B C=7.5$, $A C=9,$ and $D E=9$
<image><image_2>Find $m \angle K$ | 5
100 |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAU8AAAEXCAYAAAAtEMZoAAABRGlDQ1BJQ0MgUHJvZmlsZQAAKJFjYGASSSwoyGFhYGDIzSspCnJ3UoiIjFJgf8LAzMDHwA/E4onJxQWOAQE+QCUMMBoVfLvGwAiiL+uCzJKwP7SmjtmnLtPjr/HhLU5mmOpRAFdKanEykP4DxOnJBUUlDAyMKUC2cnlJAYjdAWSLFAEdBWTPAbHTIewNIHYShH0ErCYkyBnIvgFkCyRnJALNYHwBZOskIYmnI7Gh9oIAr4urj49CsKuRuaGl... | <image><image_1>Find the value of the variable $y$ in the figure.
<image><image_2>Find the value of $t$ in the parallelogram. | 50
7 |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAOcAAACsCAYAAACAa7uPAAABRGlDQ1BJQ0MgUHJvZmlsZQAAKJFjYGASSSwoyGFhYGDIzSspCnJ3UoiIjFJgf8LAzCABFFRjMEhMLi5wDAjwAfIYYDQq+HaNgRFEX9YFmeW62O6vsNjXJyvYZfi6dmkuxlSPArhSUouTgfQfIE5PLigqYWBgTAGylctLCkDsDiBbpAjoKCB7DoidDmFvALGTIOwjYDUhQc5A9g0gWyA5IxFoBuMLIFsnCUk8HYkNtRcEeF1cfXwUgl2NzA0t... | <image><image_1>Find the perimeter of the triangle. Round to the nearest hundredth.
<image><image_2>The segment is tangent to the circle. Find the value of $x$. | 8.73
3 |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAXwAAADwCAYAAAAD4t/dAAABRGlDQ1BJQ0MgUHJvZmlsZQAAKJFjYGASSSwoyGFhYGDIzSspCnJ3UoiIjFJgf8LAzCAKhLwMyonJxQWOAQE+QCUMMBoVfLvGwAiiL+uCzOKK+Han7EqwsuVDi8OzwwVXYqpHAVwpqcXJQPoPEKcnFxSVMDAwpgDZyuUlBSB2B5AtUgR0FJA9B8ROh7A3gNhJEPYRsJqQIGcg+waQLZCckQg0g/EFkK2ThCSejsSG2gsCvC6uPj4Kwa5G5oaW... | <image><image_1>Find the area of the shaded region. Round to the nearest tenth.
<image><image_2>Find the measure of $m \widehat{YXZ}$. | 58.9
166 |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAM4AAAD+CAYAAAByZTppAAABRWlDQ1BJQ0MgUHJvZmlsZQAAKJFjYGASSSwoyGFhYGDIzSspCnJ3UoiIjFJgf8LAzCDJwMPAyGCWmFxc4BgQ4ANUwgCjUcG3a0B1QHBZF2TWrUbLwmfhj38ssohM0zVmMsBUjwK4UlKLk4H0HyBOTy4oKmFgYEwBspXLSwpA7A4gW6QI6Cggew6InQ5hbwCxkyDsI2A1IUHOQPYNIFsgOSMRaAbjCyBbJwlJPB2JDbUXBHhdXH18FIJdjcwN... | <image><image_1>Find x.
<image><image_2>Find $y$. | 14
2 |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAOkAAAEACAYAAABWC1EdAAABRmlDQ1BJQ0MgUHJvZmlsZQAAKJFjYGASSSwoyGFhYGDIzSspCnJ3UoiIjFJgf8LAzCDJwM+gz6CZmFxc4BgQ4ANUwgCjUcG3awyMIPqyLsgszeshTVf+lEYatV4+MlVg9wlM9SiAKyW1OBlI/wHi9OSCohIGBsYUIFu5vKQAxO4AskWKgI4CsueA2OkQ9gYQOwnCPgJWExLkDGTfALIFkjMSgWYwvgCydZKQxNOR2FB7QYDXxdXHRyHY1cjc... | <image><image_1>Find x.
<image><image_2>Find y. | 8 \sqrt { 5 }
48 |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAcQAAAEgCAYAAAAqigOLAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAABl0SURBVHhe7d1PqyXXWsfx+w58ByaQeQ5kbGJeQELmtyHOm4DgrM3AgZMmNPREk4yuICQZHoQkOBC0SQ8aQcQ+OBAU6YM4aPB6cHDvFdFj/U726jz76VVVq3bt+rOe9f3AIvecXXt3X7p2/epZT9Wqn90ijP+9/uH213/y27e/+fPfuf2/39wcfgsA... | <image><image_1>Use parallelogram WXYZ to find $m\angle XYZ$
<image><image_2>Find $x$. | 105
9.5 |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAQ4AAADvCAYAAAAD3jo2AAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAABqZSURBVHhe7Z2NbxVXesb3D6kEssECBArho4mixGgjRBaLuoBSRGpV0AABRWK3pQ5aFYdtwm4akNJEWRNVSVQbJTQbki2Bxkiwu750gV0njRNMahIc4fCReIO9MTGOMQZ8385z7xz73PHcj7memTsz5/lJr4Jn5t47M+ec5zznPWcmPxBCCPEIhYMQ... | <image><image_1>Find the measure of $m\angle 2$. Assume that segments that appear
tangent are tangent.
<image><image_2>Find the perimeter of the parallelogram. Round to the nearest tenth if necessary. | 157.5
64 |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAa0AAAD0CAYAAAAooHm8AAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAABDCSURBVHhe7d2/q2zXdQdwV0mZP0EG9xa4t+MipY3+AIFDSCcMAUMCiosUaYQRuIrtNEllK0VAjW1SJE6MVYhACJFwEUgIEiGFyY9HiqRIMWFJ70jrjWfO/Lgza/Y+6/OBDe/dO3PvzDlrzvecvdfM/cwOACYhtACYhtACYBpCC4BpCC0ApiG0AJiG... | <image><image_1>Quadrilateral DEFG is a rectangle. If $m \angle EFD = 2x - 3$ and $m \angle DFG = x + 12$,
find $m \angle EFD$.
<image><image_2>Find y | 51
4 \sqrt { 2 } |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAUMAAAD9CAYAAAAmhBW2AAAuuUlEQVR4nO3de1jUZd7H8beCwSChQIQKKiLiITRRQRMKt0czO2GatbllurFu62qbT4vr02HNWl3TLXdXt7bUtdXNDqZJJzWr1QJN8ZTiCVFBxwMRIIgMyAzz/DHOj5lhgAHmzPd1XV0NMjPcHOYz3/vwu+92er1ejxBCtHHtXd0AIYRwBxKGQgiBhKEQQgAShkIIAUgYCiEEIGEohBCAhKEQQgAShkIIAUgYCiEEIGEohBCAhKEQQgAShkII... | <image><image_1>Circle $O$ has a radius of 13 inches. Radius $\overline{O B}$ is perpendicular to chord $\overline{C D}$ which is 24 inches long.
Find OX
<image><image_2>Find the area of $▱ JKLM$. | 5
24 |
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