images listlengths 1 1 | problem stringlengths 14 525 | answer stringlengths 1 112 | id int64 0 5.47k | choices null | ground_truth stringlengths 1 112 |
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{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAf4AAAHsCAYAAAAzcc+1AACOmElEQVR4nOzdd3hb15nv++9GbwRAgATATqpbXbKqe42dZqc4PXESp0xJTqadzJzJnHPnzJly75RMOZOZSeJUp/fiOIlLYlu2JVnFlmT1QrETAEkQANHL3vcPgCBlq4sFJN/P82gccSRwiyT2b693rfUuRdM0DSGEEEIsCLrZvgAhhBBCzBwJfiGEEGIBkeAXQgghFhAJfiGEEGIBkeAXQgghFhAJfiGEEGIBkeAXQgghFhAJfiGEEGIBkeAX... | <image>H K and I G are diameters of \odot L. Find m \widehat H I. | B | 900 | null | B |
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{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAkUAAAH0CAYAAAAzAFmMAADepElEQVR4nOzddXxb973/8deRdMSWmSkx22mStmmbMjOso3I77h3T3e7g/sZbt7vdMd/xVtqKKzOlTElD5ji2Y2ZbTOf8/pAsc2I7ThPbn+ce7dpGlhRH1nnr+/18Px9F13UdIYQQQohVznC4n4AQQgghxJFAQpEQQgghBBKKhBBCCCEACUVCCCGEEICEIiGEEEIIQEKREEIIIQQgoUgIIYQQApBQJIQQQggBSCgSQgghhAAkFAkhhBBCABKK... | <image>Find x. | B | 901 | null | B |
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{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAlMAAAEyCAYAAADeAVWKAAAt4ElEQVR4nO3df3hU9Zn38Vtp2AUvIN0QwISE0JoECGIqJCRR7CIYCY9eYn2kWm0EIy2lTQuUYrXJcmFYWigCW/xBC1HKaqUgS7nsoiYozwKGkIEsggGS6BIGErAhT5N4xT7brMvzB5shZ36emXNmzq/366+ew2TytSTDZ+65v9/7hqtXr14VAAAARORGoxcAAABgZYQpAAAADQhTAAAAGhCmAAAANCBMAQAAaECYAgAA0IAwBQAAoAFhCgAA... | <image>If T P = 4 x + 2, Q P = 2 y - 6, P S = 5 y - 12, and P R = 6 x - 4, find x so that the quadrilateral is a parallelogram. | B | 902 | null | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAQoAAAEECAYAAADQwXq5AAABRmlDQ1BJQ0MgUHJvZmlsZQAAeJxjYGASSSwoyGFhYGDIzSspCnJ3UoiIjFJgf8LAzCDNwMvAxcCWmFxc4BgQ4ANUwgCjUcG3awyMIPqyLsgsobSDM7jnPHqnzpEXkd/omY2pHgVwpaQWJwPpP0CcnlxQVMLAwJgCZCuXlxSA2B1AtkgR0FFA9hwQOx3C3gBiJ0HYR8BqQoKcgewbQLZAckYi0AzGF0C2ThKSeDoSG2ovCPC6uPr4KAS7Gpkb... | <image>Find x. | D | 903 | null | D |
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{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAA2AAAAGyCAYAAACC+6epAADu7UlEQVR4nOz9d3Cc5xXveX4754TYQCODAQxgDiAVqJwl25JlWcFBVrJ979x7Z2erdmZ2difsnd25NVU7OzV3bEuWZMlRtoKtLFE5kARzDiBBIjbQyJ1z97t/dCOQYgDACOB8qliSIABsAI1+n/M+5/kdlaIoCkIIIYQQQgghLjv11X4AQgghhBBCCDFXSAEmhBBCCCGEEFeIFGBCCCGEEEIIcYVIASaEEEIIIYQQV4gUYEIIIYQQQghxhUgB... | <image>\triangle R S T \cong \triangle X Y Z. Find x. | D | 904 | null | D |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAcoAAAEFCAYAAABjIqe9AAABRmlDQ1BJQ0MgUHJvZmlsZQAAeJxjYGASSSwoyGFhYGDIzSspCnJ3UoiIjFJgf8LAzCDEwMVgyqCVmFxc4BgQ4ANUwgCjUcG3awyMIPqyLsis3Utj/vW8f8nssnDSwp/ruCwx1aMArpTU4mQg/QeI05MLikoYGBhTgGzl8pICELsDyBYpAjoKyJ4DYqdD2BtA7CQI+whYTUiQM5B9A8gWSM5IBJrB+ALI1klCEk9HYkPtBQFeF1cfH4VgVyNz... | <image>Find x if A D is an altitude of \triangle A B C. | D | 905 | null | D |
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{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAd0AAAG2CAYAAAA6Dlz3AABumklEQVR4nO3dd5xcV3n/8c+dPjsz23tf9S5LsmXZltx7N4aEGif0YiA/IFQDIdQEUkiABBKHUAzYBlzk3rtlWb237b3O7PR67++PKburunV2Zvd5vxCypN3VaGfmfu855znPUTRN0xAZI9b6IF/99L/y5P5u/JqCdcEdfO2fP8fNa6qw62f70QkhhJgKw2w/ADFajLY3t3FkIEze6mv5i3e8h3fddAELim0Yldl+bEIIIaZKkZFuZtGCPbT2... | <image>In A, the radius is 14 and C D = 22. Find E B. Round to the nearest hundredth. | B | 906 | null | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAQsAAADSCAYAAABdE+UBAAABRWlDQ1BJQ0MgUHJvZmlsZQAAeJxjYGASSSwoyGFhYGDIzSspCnJ3UoiIjFJgf8LAzCDJwMPAyGCWmFxc4BgQ4ANUwgCjUcG3a0B1QHBZF2TWrUbLwmfhj38ssohM0zVmMsBUjwK4UlKLk4H0HyBOTy4oKmFgYEwBspXLSwpA7A4gW6QI6Cggew6InQ5hbwCxkyDsI2A1IUHOQPYNIFsgOSMRaAbjCyBbJwlJPB2JDbUXBHhdXH18FIJdjcwN... | <image>Find x. Round to the nearest degree. | C | 907 | null | C |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAT8AAAD8CAYAAAABraMFAAAYnElEQVR4nO3de1xUdf7H8fcIiFzCQIlsQFERKPECoVZ429K8JaJuW6n109LKRFt/rra/zOxmu3nJEtJaTdK1WrXwJ7vrPVdTVkUTL7SCYKYwyyIKhFzlMvsHHoRhgGHmzJwz830/H48ej3SG4QsPePk9Z2bOR6PX6/UgIhJMO6UXQESkBMaPiITE+BGRkBg/IhIS40dEQmL8iEhIjB8RCYnxIyIhMX5EJCTGj4iExPgRkZAYPyISEuNHREJi... | <image>Find x. | B | 908 | null | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAoAAAAGfCAYAAADPpWPwAACKuElEQVR4nOzddXhUV97A8e+4R4knQHAv7qXQUqy0xT1AXdd337Xatt3drlvdgeAOLS6luLuTIBHiNpPJ6J33jwClJbRIIPb7PM8++7SdTE5gMvc75957jioQCAQQQgghhBB1hrqqByCEEEIIIe4uCUAhhBBCiDpGAlAIIYQQoo6RABRCCCGEqGMkAIUQQggh6hgJQCGEEEKIOkYCUAghhBCijpEAFEIIIYSoYyQAhRBCCCHqGAlAIYQQQog6... | <image>Find A F. | B | 909 | null | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAARIAAAFfCAYAAACC8UORAAABRmlDQ1BJQ0MgUHJvZmlsZQAAeJxjYGASSSwoyGFhYGDIzSspCnJ3UoiIjFJgf8LAzCDEwMVgyqCVmFxc4BgQ4ANUwgCjUcG3awyMIPqyLsis3Utj/vW8f8nssnDSwp/ruCwx1aMArpTU4mQg/QeI05MLikoYGBhTgGzl8pICELsDyBYpAjoKyJ4DYqdD2BtA7CQI+whYTUiQM5B9A8gWSM5IBJrB+ALI1klCEk9HYkPtBQFeF1cfH4VgVyNz... | <image>In \triangle P Q R, Z Q = 3 a - 11, Z P = a + 5, P Y = 2 c - 1, Y R = 4 c - 11, m \angle P R Z = 4 b - 17, m \angle Z R Q = 3 b - 4, m \angle Q Y R = 7 b + 6, and m \angle P X R = 2 a + 10. P X is an altitude of \triangle P Q R. Find a. | D | 910 | null | D |
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{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAYwAAAE4CAYAAABIYsQpAAABRmlDQ1BJQ0MgUHJvZmlsZQAAeJxjYGASSSwoyGFhYGDIzSspCnJ3UoiIjFJgf8LAzMDHIMQgw8CdmFxc4BgQ4ANUwgCjUcG3awyMIPqyLsisy79j76nNu7c/WdpE/GtOzxpM9SiAKyW1OBlI/wHi9OSCohIGBsYUIFu5vKQAxO4AskWKgI4CsueA2OkQ9gYQOwnCPgJWExLkDGTfALIFkjMSgWYwvgCydZKQxNOR2FB7QYDXxdXHRyHY1cjc... | <image>In the figure, m \angle 4 = 104, m \angle 14 = 118. Find the measure of \angle 7. | B | 911 | null | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAlcAAAF5CAYAAACydQ9fAABUwElEQVR4nO3df2xTd94v+Hd3uav0qnCaalmJUrtJQWjL2pCnXabPrdMERrdUcQTxc2euJsnNKKFXD3GaoU2nw2SVh1voiGGVMr1Nh0mT9O5AoubGfjR0rgElEfTZp0Dj7vRBnQnYSiVUfvSYFGmRSE7SfRLpiS77hzkn5xz/to/tY/v9kirhg33yjYuPP+f7/Xw/n0cePHjwAERERERkiP8h3wMgIiIiKiYMroiIiIgMxOCKiIiIyEAMroiI... | <image>Find m \angle D. | A | 912 | null | A |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAZkAAADsCAYAAACmPdsIAAABRWlDQ1BJQ0MgUHJvZmlsZQAAeJxjYGASSSwoyGFhYGDIzSspCnJ3UoiIjFJgf8LAzCDOwMvAxsCemFxc4BgQ4ANUwgCjUcG3awyMIPqyLsgsXtuav29kL2vyZafUn/EoiMBUjwK4UlKLk4H0HyBOTy4oKmFgYEwBspXLSwpA7A4gW6QI6Cggew6InQ5hbwCxkyDsI2A1IUHOQPYNIFsgOSMRaAbjCyBbJwlJPB2JDbUXBHhdXH18FIJdjcwN... | <image>Find x. | C | 913 | null | C |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAZMAAAClCAYAAACZSBBlAAABRmlDQ1BJQ0MgUHJvZmlsZQAAeJxjYGASSSwoyGFhYGDIzSspCnJ3UoiIjFJgf8LAzCDGIM6gz2CQmFxc4BgQ4ANUwgCjUcG3awyMIPqyLsgs+VNVf877TN/6iLfO3WPuVBNM9SiAKyW1OBlI/wHi9OSCohIGBsYUIFu5vKQAxO4AskWKgI4CsueA2OkQ9gYQOwnCPgJWExLkDGTfALIFkjMSgWYwvgCydZKQxNOR2FB7QYDXxdXHRyHY1cjc... | <image>For the pair of similar figures, find the area of the green figure. | D | 914 | null | D |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAUkAAAFHCAYAAAAsgL7YAAABRWlDQ1BJQ0MgUHJvZmlsZQAAeJxjYGASSSwoyGFhYGDIzSspCnJ3UoiIjFJgf8LAzCDOwMvAxsCemFxc4BgQ4ANUwgCjUcG3awyMIPqyLsgsXtuav29kL2vyZafUn/EoiMBUjwK4UlKLk4H0HyBOTy4oKmFgYEwBspXLSwpA7A4gW6QI6Cggew6InQ5hbwCxkyDsI2A1IUHOQPYNIFsgOSMRaAbjCyBbJwlJPB2JDbUXBHhdXH18FIJdjcwN... | <image>Find x. | D | 915 | null | D |
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{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAnoAAAI1CAYAAABBpFe1AADVs0lEQVR4nOz9d1zUabvn+36qyKHIhYJiREBBJQdzbG21zd222X7WmrVm1uyZfWatSWfPeZ2z9+ucnWbPmrDWnlnzzKzn6TZ3t1nbtrXNiZyUpKJkkSpykalw/gB+AtqKChQU1/v16j+eerC4Uaj6ct/XfV0qi8ViQQghhBBCjB0WC2aTEaPJhMlswtjVhdGixt7BEQd7e+zt7bGzU6F6z9OoJOgJIYQQQtgmtbUXIIQQQgghRoa9tRcghBBC... | <image>P is the centroid of triangle Q U S. If Q P = 14 centimeters, what is the length of Q T? | D | 916 | null | D |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAcIAAAGWCAYAAADrB4OkAAB4t0lEQVR4nO3dd3xV9f3H8de5e2bvBRkQtiAIqCggiOKoo3W2WvurrW21tdZaO2zVWltrl1bb2t0qdW9xoIIIiuJij5AFCdk7uXuc8/vjJjeJgrIybu7n+XhQBIFeyb3nfb6f8/1+PoqmaRpCCCFEnNKN9AsQQgghRpIEoRBCiLgmQSiEECKuSRAKIYSIaxKEQggh4poEoRBCiLgmQSiEECKuSRAKIYSIaxKEQggh4poEoRBCiLgmQSiEECKu... | <image>The segment is tangent to the circle. Find x. | C | 917 | null | C |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAlMAAAD9CAYAAACYyPJfAAAqLElEQVR4nO3df3wU9b3v8U/7OI/bP24LzdkHnFtB6innkAi2NUoS5UgiSWhjCEKCBlMk0CZBjaj5ITHakJCAFtAkWCWKIT0QpEgsAgIppssigYuJAbXaJGrveVxIAj1Xr7fMes/9o/94/+AQdyazye7O7s7Mzuv5Fzv7gy+Q/fKeme/38/nGV1999ZUAAAAgJN80ewAAAAB2RpgCAAAwgDAFAABgAGEKAADAAMIUAACAAYQpAAAAAwhTAAAA... | <image>Quadrilateral A B C D is shown. A C is 40 and B D is \frac { 3 } { 5 } A C. B D bisects A C. For what value of x is A B C D a parallelogram. | C | 918 | null | C |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAWIAAAEPCAYAAAB4Ns7+AABPl0lEQVR4nO2deViU5feHbzbZFQEVARXBBXHJBbUQNUErTTHXtDTTLMvKcinTMjNbzNTKfuVWLmXp1zWXMnPLDTXXXJBEEBAEEZB9EWbm98c4wwzrALMx89zX5dXQvAPPzLzzmfOe55zPsSguuCNDIBAIBAbD0tALEAgEAnNHCLFAIBAYGCHEAoFAYGCEEAsEAoGBEUIsEAgEBkYIsUAgEBgYIcQCgUBgYIQQCwQCgYERQiwQCAQGRgixQCAQ... | <image>Find m \widehat B C A. | D | 919 | null | D |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAb4AAAEGCAYAAAAaFPDxAAABRWlDQ1BJQ0MgUHJvZmlsZQAAeJxjYGASSSwoyGFhYGDIzSspCnJ3UoiIjFJgf8LAzCDOwMvAxsCemFxc4BgQ4ANUwgCjUcG3awyMIPqyLsgsXtuav29kL2vyZafUn/EoiMBUjwK4UlKLk4H0HyBOTy4oKmFgYEwBspXLSwpA7A4gW6QI6Cggew6InQ5hbwCxkyDsI2A1IUHOQPYNIFsgOSMRaAbjCyBbJwlJPB2JDbUXBHhdXH18FIJdjcwN... | <image>Find the value of the variable w. | B | 920 | null | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAVcAAAEWCAYAAADSNdTRAAABRGlDQ1BJQ0MgUHJvZmlsZQAAeJxjYGASSSwoyGFhYGDIzSspCnJ3UoiIjFJgf8LAzCAKhLwMyonJxQWOAQE+QCUMMBoVfLvGwAiiL+uCzOKK+Han7EqwsuVDi8OzwwVXYqpHAVwpqcXJQPoPEKcnFxSVMDAwpgDZyuUlBSB2B5AtUgR0FJA9B8ROh7A3gNhJEPYRsJqQIGcg+waQLZCckQg0g/EFkK2ThCSejsSG2gsCvC6uPj4Kwa5G5oaW... | <image>In the figure, the vertices of quadrilateral A B C D intersect square E F G H and divide its sides into segments with measure that have a ratio of 1:2. Find the ratio between the areas of A B C D and E F G H. | C | 921 | null | C |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAykAAAE8CAYAAADE7v5rAACKH0lEQVR4nO3deViU5frA8S8Ou4CAIqiIgIAbmhvuJplLaqlpq2bLL9vVY8e0sk7LKTul2WbHsjxtlra5tZlLpuaW5JLiBoqIoCgKCCMDDMP8/hiYhWVmgIGZgftzXV0Xz/DOzCsNvO/93M99Py5arVaLEEIIIYQQQjiIZvY+ASGEEEIIIYQwJkGKEEIIIYQQwqFIkCKEEEIIIYRwKBKkCCGEEEIIIRyKBClCCCGEEEIIhyJBihBCCCGEEMKh... | <image>Each pair of polygons is similar. Find x. | C | 922 | null | C |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAANUAAADdCAYAAAAsEzfuAAAo5UlEQVR4nO2dfViUZdr/Py4QoIiCIiIoCCiIaIKibpC4PVr2spJYuVmZbqzbmtb6K33crNV2H3ssMyutts0yrUe3LBRrs9ItTHwDFF9QEUHeBhEREEQGYsb5/THMzfA+wD3v1+c4PI6Z4Z77vpyZ732e13md53n10mg0GgQCgWz8ytwDEAhsDSEqgUBmhKgEApkRohIIZEaISiCQGSEqgUBmhKgEApkRohIIZEaISiCQGSEqgUBmhKgEApkR... | <image>In \odot B, the diameter is 20 units long, and m \angle A C E = 45. Find x. | A | 923 | null | A |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAnMAAAFtCAYAAABshOx4AAChfElEQVR4nOz9V5BcV5buef6Pe7jWKrTWAloTAAEQIARBnazMLJFZVT11+3b3tX5pm26zeRqzeZ3nnrE2655blVW3VGZlUpMASRAgCK1VaK3Dw7XW58yDRwCgAAiACCAisH8PacZIhMcJ4cc/33uvtSRFURQEQRAEQRCEFUn1vC9AEARBEARBeHIizAmCIAiCIKxgIswJgiAIgiCsYCLMCYIgCIIgrGAizAmCIAiCIKxgIswJgiAIgiCsYCLM... | <image>Find m \angle 2. | B | 924 | null | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAOUAAACfCAYAAAAGcB6xAAAPlElEQVR4nO3dbVhUZR4G8HsWRkRMS0U0IUkw0YXEVq0WXLfMsGxRc3NX0sqktoxqzcxaN01bd9UyXfWyaxUj18yrNS3dtsK0VcNe1MQEFV9wKeUyREVwEHAYzn5AhpkJlJlzzpznOXP/vk3zwqmne85wnnv+WBRFUUBEwviZ0QdARO4YSiLBMJREgmEoiQTDUBIJhqEkEgxDSSQYhpJIMAwlkWAYSiLBMJQSqKqpxcCZ23GytNLoQyE/YCgF... | <image>Find x. | A | 925 | null | A |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAUgAAADsCAYAAAAW7j9/AAABRmlDQ1BJQ0MgUHJvZmlsZQAAeJxjYGASSSwoyGFhYGDIzSspCnJ3UoiIjFJgf8LAzCDKwM8gxsCSmFxc4BgQ4ANUwgCjUcG3awyMIPqyLsisC7aSmesmMSxXbTvSeH32L15M9SiAKyW1OBlI/wHi9OSCohIGBsYUIFu5vKQAxO4AskWKgI4CsueA2OkQ9gYQOwnCPgJWExLkDGTfALIFkjMSgWYwvgCydZKQxNOR2FB7QYDXxdXHRyHY1cjc... | <image>Find the area of the quadrilateral. | C | 926 | null | C |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAc4AAAGZCAYAAAAAbdH/AAChEUlEQVR4nOzdd3jUVdbA8e/0THqHFDop9N47UqRIEVCkSUekY1vru666uipdkI4IigoqUpXee++kUJKQkN5nMpn2/pHkRwIWAmmT3M/z8OwuSyaTzMw995577rkyq9VqRRAEQRCExyIv7ScgCIIgCLZEBE5BEARBKAQROAVBEAShEETgFARBEIRCEIFTEARBEApBBE5BEARBKAQROAVBEAShEETgFARBEIRCEIFTEARBEApBBE5BEARBKAQR... | <image>If m \angle A E D = 95 and m \widehat A D = 120, what is m \angle B A C? | B | 927 | null | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAN8AAACpCAYAAACrgujwAAAcJ0lEQVR4nO2de0CUVd6AH9bxgo4IuDAqqICAaKiQgG7S4mepaSYmuZWl5ZfdTNts10tZuVbupmSWl9pP6XPTVttcb61flrquFzQTLwgTIiCCDioiA4zgMDnG98cwI/frzLzvDOf5j5l33jnz8j7vOed3zvkdl4qKigoEAoHd+ZXUBRAI2ipCPoFAIoR8AoFECPkEAokQ8gkEEiHkEwgkQsgnEEiEkE8gkAghn0AgEUI+gUAihHwCgUQI+QQC... | <image>Find x. Assume that segments that appear to be tangent are tangent. | A | 928 | null | A |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAqgAAAGwCAYAAABl1Zc3AACusElEQVR4nOzddXTc953v/+d3eDQ8YpaZYojZThzGNk0hbZpSiilsd9u9tL27v3t37+7de5e7t7BlSpsGGmwbRidOYseQmBnEPMz4/f0xo9FIRsmyNZLej3NyLKupoyijmdd8Pm9QVFVVEUIIIYQQokRoJvsLEEIIIYQQopgEVCGEEEIIUVIkoAohhBBCiJIiAVUIIYQQQpQUCahCCCGEEKKkSEAVQgghhBAlRQKqEEIIIYQoKRJQhRBCCCFE... | <image>Assume that the segment is tangent, find the value of x. | C | 929 | null | C |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAhUAAAHYCAYAAAD6ehqJAADERUlEQVR4nOz9Z3RcZ57neX5veAsTAUQEvAcJD9BTlCflJcpS3mVmVXW1m+mZ7p3pmdk90/Nizp7pntne3u6e7qqsNEqZTHnvLSVKogXhPQgQNiwQAMK7uy8CdBJJ0YCE4fM5p+pUkcEHN6CIG/94zP8nybIsIwiCIAiCcJkUy30BgiAIgiCsDaKoEARBEARhSYiiQhAEQRCEJSGKCkEQBEEQloQoKgRBEARBWBKiqBAEQRAEYUmIokIQBEEQ... | <image>Find X Y. | A | 930 | null | A |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAN8AAAFDCAYAAAC6KtugAAABRGlDQ1BJQ0MgUHJvZmlsZQAAeJxjYGASSSwoyGFhYGDIzSspCnJ3UoiIjFJgf8LAzCAEFGRmEEhMLi5wDAjwAfIYYDQq+HaNgRFEX9YFmXXT7Mim4rkXSq/kTk22YHhQjKkeBXClpBYnA+k/QJyeXFBUwsDAmAJkK5eXFIDYHUC2SBHQUUD2HBA7HcLeAGInQdhHwGpCgpyB7BtAtkByRiLQDMYXQLZOEpJ4OhIbai8I8Lq4+vgoBLsamRta... | <image>\triangle K L N and \triangle L M N are isosceles and m \angle J K N = 130. Find the measure of \angle L N M. | B | 931 | null | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAARMAAAC2CAYAAAD6D2lRAAABRGlDQ1BJQ0MgUHJvZmlsZQAAeJxjYGASSSwoyGFhYGDIzSspCnJ3UoiIjFJgf8LAzCAEFGRmEEhMLi5wDAjwAfIYYDQq+HaNgRFEX9YFmXXT7Mim4rkXSq/kTk22YHhQjKkeBXClpBYnA+k/QJyeXFBUwsDAmAJkK5eXFIDYHUC2SBHQUUD2HBA7HcLeAGInQdhHwGpCgpyB7BtAtkByRiLQDMYXQLZOEpJ4OhIbai8I8Lq4+vgoBLsamRta... | <image>Given right triangle X Y Z with hypotenuse X Y, Y P is equal to Y Z. If m \angle P Y Z = 26, find m \angle X Z P. | A | 932 | null | A |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAfQAAAFaCAYAAADowK8UAAA3eElEQVR4nO3df1gUV5ov8NdxyIxxxd4A0UAgjA6NCtEM2ASQOBsNRL3JqOvIkBjxB5rrZgfjKrozPnLzuBgzk6iPkUnGjeIPErMGx2ucyUYlUe8YAoSWjBIQgTWLtBCJkDQw6sZel/sHdMOpqqZ/VXdVnfp+/koVdHGeJPCeOue87zust7e3lwAAAEDTvqf0AAAAAMB3COgAAAAcQEAHAADgAAI6AAAABxDQAQAAOICADgAAwAEEdAAAAA4g... | <image>A B C D is a rhombus. If E B = 9, A B = 12 and m \angle A B D = 55. Find m \angle B D A. | D | 933 | null | D |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAdgAAAFZCAYAAAA7NT7kAAABRmlDQ1BJQ0MgUHJvZmlsZQAAeJxjYGASSSwoyGFhYGDIzSspCnJ3UoiIjFJgf8LAzCDAIMjAxaCYmFxc4BgQ4ANUwgCjUcG3awyMIPqyLsisAzE/mqMZRJ9vLbg2Z0nKum2Y6lEAV0pqcTKQ/gPE6ckFRSUMDIwpQLZyeUkBiN0BZIsUAR0FZM8BsdMh7A0gdhKEfQSsJiTIGci+AWQLJGckAs1gfAFk6yQhiacjsaH2ggCvi6uPj0Kwq5G5... | <image>In the figure, m \angle 3 = 110 and m \angle 12 = 55. Find the measure of \angle 15. | B | 934 | null | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAUIAAAD1CAYAAAAlFfzlAAA9pklEQVR4nO2deVxUZRfHvyOigLiAIiEo+6agiWuiSYWpaa6VaYtZ2ltqpZm+vlppmWZqm1laaVqpZaapZaWSYYqaC4igyCoqRMi+yOIw3PePAYRhgGEZZoZ5vp+Pn8/gXebMzL2/+zznnOccmSRJEgKBQGDEtNK1AQKBQKBrhBAKBAKjRwihQCAweoQQCgQCo0cIoUAgMHqEEAoEAqNHCKFAIDB6hBAKBAKjRwihQCAweoQQCgQCo6e1rg3Q... | <image>Find m \angle F. | D | 935 | null | D |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAVMAAAEACAYAAAAOUZUtAAABRGlDQ1BJQ0MgUHJvZmlsZQAAeJxjYGASSSwoyGFhYGDIzSspCnJ3UoiIjFJgf8LAzCAKhLwMyonJxQWOAQE+QCUMMBoVfLvGwAiiL+uCzOKK+Han7EqwsuVDi8OzwwVXYqpHAVwpqcXJQPoPEKcnFxSVMDAwpgDZyuUlBSB2B5AtUgR0FJA9B8ROh7A3gNhJEPYRsJqQIGcg+waQLZCckQg0g/EFkK2ThCSejsSG2gsCvC6uPj4Kwa5G5oaW... | <image>Rhombus R S T U has an area of 675 square meters. Find S U. | D | 936 | null | D |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAARsAAADNCAYAAACIPdSnAAABRmlDQ1BJQ0MgUHJvZmlsZQAAeJxjYGASSSwoyGFhYGDIzSspCnJ3UoiIjFJgf8LAzMDHIMQgw8CdmFxc4BgQ4ANUwgCjUcG3awyMIPqyLsisy79j76nNu7c/WdpE/GtOzxpM9SiAKyW1OBlI/wHi9OSCohIGBsYUIFu5vKQAxO4AskWKgI4CsueA2OkQ9gYQOwnCPgJWExLkDGTfALIFkjMSgWYwvgCydZKQxNOR2FB7QYDXxdXHRyHY1cjc... | <image>Find the value of x in the figure below. | D | 937 | null | D |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAfQAAAFaCAYAAADowK8UAAA3eElEQVR4nO3df1gUV5ov8NdxyIxxxd4A0UAgjA6NCtEM2ASQOBsNRL3JqOvIkBjxB5rrZgfjKrozPnLzuBgzk6iPkUnGjeIPErMGx2ucyUYlUe8YAoSWjBIQgTWLtBCJkDQw6sZel/sHdMOpqqZ/VXdVnfp+/koVdHGeJPCeOue87zust7e3lwAAAEDTvqf0AAAAAMB3COgAAAAcQEAHAADgAAI6AAAABxDQAQAAOICADgAAwAEEdAAAAA4g... | <image>A B C D is a rhombus. If E B = 9, A B = 12 and m \angle A B D = 55. Find A E. | A | 938 | null | A |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAlQAAAGqCAYAAADN6NrdAACcGElEQVR4nOz9ZZhcZ5rue/5XMCcHJoiZIcUyM9tlZiwXNOzde++ZM2fOnGuumbkOde/d1d0FdpmZq1xmlsWpFDNLSRGRnMEcaz5ESCbZlpQpJT2/b7aUESsVmbHuWO+z7ldRVVVFCCGEEEKcNc1gH4AQQgghxHAngUoIIYQQop8kUAkhhBBC9JMEKiGEEEKIfpJAJYQQQgjRTxKohBBCCCH6SQKVEEIIIUQ/SaASQgghhOgnCVRCCCGEEP0k... | <image>Find m \angle 2. | C | 939 | null | C |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAi8AAAFDCAYAAADyCu74AAAr10lEQVR4nO3db2wb953n8a+7voONbTK2u8EhzZF17cIPcuTF2CLAwcPKyfYAQ9LZ0UNJ68LpE4vaXLsKCleA6gcK4DWgGD0o6fpEBQesjQgiH9otLCEGisYO6cMh6KEBiT4w6j8Z4pIDgo08ueKiA7zQPZBnPBySoxlyOH/fr0eSTFETRdJ8+f39fp/vrq2trS0BAACIiW+EfQEAAABeULwAAIBYoXgBAACxQvECAABiheIFAADECsULAACI... | <image>Quadrilateral A B D C is a rectangle. Find m \angle 6 if m \angle 1 = 38. | A | 940 | null | A |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAdwAAAHNCAYAAAC0KcrLAACWwklEQVR4nOzddXhb2bX38e8RS5bMlmQIOZwJwzBksMM8k+G2M7e95fYt8y1zb3uLU5h2OpBhZuZkZsLMHJPMYp2jc877h5zEFDZI9vo8T5/n3tZ2FMc+P+219l5bMU3TRAghhBD9yjLYL0AIIYQYDiRwhRBCiAEggSuEEEIMAAlcIYQQYgBI4AohhBADQAJXCCGEGAASuEIIIcQAkMAVQgghBoAErhBCCDEAJHCFEEKIASCBK4QQQgwACVwh... | <image>Find y. | B | 941 | null | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAnAAAAFzCAYAAAC+bzSQAADAnUlEQVR4nOz913tc+Xnoe35X5ZyrUMiRJAjmzGbsZuesblmSJUtO++wzc54zz8y5nv9hLmfmmZltb1uSbVmS1TknpmbOGSByFVLlnKvWXBQIokgwJ4Tf58KPxQbJIlC11rt+b5JkWZYRBEEQBEEQFgzFs34BgiAIgiAIwoMRAZwgCIIgCMICIwI4QRAEQRCEBUYEcIIgCIIgCAuMCOAEQRAEQRAWGBHACYIgCIIgLDAigBMEQRAEQVhgRAAn... | <image>Use parallelogram J K L M to find m \angle J M L. | C | 942 | null | C |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAhsAAAG+CAYAAAA6HsZ9AADew0lEQVR4nOzddZgc15Xw4V9Vc/cw80galEbMshjMzGzHdhLHcfjLJtnNbnaDm2zAjh2wY46ZUZYssmQxMwwz8zRDVX1/1Ghkx4KRNKz7Po8TW1PdfWvUXX3q3nPPkTRN0xAEQRAEQegn8mAPQBAEQRCEkU0EG4IgCIIg9CsRbAiCIAiC0K9EsCEIgiAIQr8SwYYgCIIgCP1KBBuCIAiCIPQrEWwIgiAIgtCvRLAhCIIgCEK/EsGGIAiCIAj9... | <image>Use parallelogram A B C D to find m \angle A F B. | D | 943 | null | D |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAR8AAAETCAYAAAAPlQI2AAAgBElEQVR4nO3df1CU950H8LdKwpIQlrVHepqygFraU4jG1HYajGB/aNRJoHM3LXj2wPsVo01D28t4Y7xxc6Pe5dIf5Hox2v4hXB3hbqZTSCZavLlzMW6mCXfeJlA7YwRXqCGnLcsDtqxxDffH8jw8u+zvfX4/79dMZhCehUcDb77f7+f5fL8LZmZmZkBEpLGFet8AEdkTw4eIdMHwISJdMHyISBcMHyLSBcOHiHTB8CEiXTB8iEgXDB8i0gXD... | <image>Find W T, if Z X = 20 and T Y = 15. | A | 944 | null | A |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAZsAAAD3CAYAAADL2fltAAABRWlDQ1BJQ0MgUHJvZmlsZQAAeJxjYGASSSwoyGFhYGDIzSspCnJ3UoiIjFJgf8LAzCDOwMvAxsCemFxc4BgQ4ANUwgCjUcG3awyMIPqyLsgsXtuav29kL2vyZafUn/EoiMBUjwK4UlKLk4H0HyBOTy4oKmFgYEwBspXLSwpA7A4gW6QI6Cggew6InQ5hbwCxkyDsI2A1IUHOQPYNIFsgOSMRaAbjCyBbJwlJPB2JDbUXBHhdXH18FIJdjcwN... | <image>Find x. | C | 945 | null | C |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAR0AAAD9CAYAAACBWaNNAAArQElEQVR4nO3de1jUZf7/8acLLKIIAiEeEBERUdFERU0o3VYz2xLTrNUt0w3b3dJ2/e5ibtaa2+qWVpbZaXWztNXMTaVarfRXWnjE1AQNAQUVRERBDjIQ4Pz+GGeYgQEGmPnMfGbej+vqugYZ4I7Da+7T+77babVaLUIIoZCf2bsBQgjXIqEjhFCUhI4QQlESOkIIRUnoCCEUJaEjhFCUhI4QQlESOkIIRUnoCCEUJaEjhFCUhI4QQlESOkII... | <image>In \odot A, m \angle E A D = 42. Find m \widehat E D B. | C | 946 | null | C |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAhAAAAICCAYAAACeHvQZAAC5IElEQVR4nOzdd3hb93Xw8e+92CBAABwANylqS9b23iNxbMfO3klHusfbtE2TprvpbtN0v2m60qZ5M9osJ7YTO957a+9JEeDAILH3uu8fFwRJWbZFihTX+TyPHoWMCF9R4MXB+Z2haJqmIYQQQggxA+pCX4AQQgghlh4JIIQQQggxYxJACCGEEGLGJIAQQgghxIxJACGEEEKIGZMAQgghhBAzJgGEEEIIIWZMAgghhBBCzJgEEEIIIYSYMQkg... | <image>P M is a diameter of \odot R. Find m \widehat M N P. | D | 947 | null | D |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAkgAAAG5CAYAAAB1OMuOAACqF0lEQVR4nOzdd3hUZdrH8e850ycz6RB6J6RgQxQL9o4FK4gNxd5d26666q7rrr5rL2vDXpBiVyxgQ0WUKiWVJEDoISFlJpl6znn/mJRJaAEDzIT7c11e14KQzJozZ37nfp7nvhXDMAyEEEIIIUQzdW+/ACGEEEKIWCMBSQghhBCiDQlIQgghhBBtSEASQgghhGhDApIQQgghRBsSkIQQQggh2pCAJIQQQgjRhgQkIYQQQog2JCAJIYQQQrQh... | <image>Find S R. | B | 948 | null | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAQcAAADsCAYAAAB5X2NSAAAvw0lEQVR4nO2de1xUdfrH38SwiAIKiIiMgoKIiqYoakLKtmrZTdPMze1im921zS392V3btTXZytLulGZla6ZGtWnqlhSYiuJtVOQugooICCKXYDi/P8Y5zMAAg86FOfN9v169OuCZmS8zZz7nuX2fx6Wurk5CIBAImnCNvRcgEAg6JkIcBAKBSVTXXCP0QSAQNEcog0AgMIkQB4FAYBKVi4uLvdcgEAg6IMJyEAgEJhHiIBAITCLcCoFAYBKV... | <image>Find m \angle A G E. | B | 949 | null | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAVkAAADBCAYAAABlsMNBAAAwwklEQVR4nO3deViU1f//8ScJKogoKKKBioAKimuCFZpWqLkkqKVpZlZaaZbyNcy0X7aomUtallpaLrmbBH4qS80wQVTMFTdwQR1SRFbRAQHn9wfNyDLDOsPMwPtxXV4XyD0zhxt4zbnPed/nWKhUKhVCCCEM4iFjN0AIIaozCVkhhDAgCVkhhDAgCVkhhDAgCVkhhDAgCVkhhDAgCVkhhDAgCVkhhDAgCVkhhDAgCVkhhDAgS2M3QFRH98m6... | <image>Find x. Assume that any segment that appears to be tangent is tangent. | A | 950 | null | A |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAPoAAADRCAYAAADlh6/IAAAhL0lEQVR4nO3de1xUdf7H8RcC6ShCgkQsmKDgJdHURFth091VUbt417TSLma66uYltdQyW9dfaWVualtieCkvuSWmqXgpTdEUS1MML2BeMCRkVEQHgnF+f+BMAw7IMLcznM/z8ejxKDjgSXjP98z3vM/362EwGAwIIaq1Gq4+ASGE40nQhVABCboQKiBBF0IFJOhCqIAEXQgVkKALoQISdCFUQIIuhApI0IVQAQm6ECogQRdCBSToQqiABF0I... | <image>Use rhombus X Y Z W with m \angle W Y Z = 53, V W = 3, X V = 2 a - 2, and Z V = \frac { 5 a + 1 } { 4 }. Find X Z. | C | 951 | null | C |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAARYAAAERCAYAAAC+SIj3AAA+VUlEQVR4nO2deVyU5fr/3zCObLLIJoIigijikguVkkumntLMMrVjv7TUOrZ4jnXMk9W35ZSnso7Hym+rLVra106alplWbmVGpaiYiguCiGziMAIDDOMww++PcYYZGGCAWR5m7vfr5es1I88wNzPP83mu63Nf93V71dYU1iEQCAR2xNvVAxAIBO6HEBaBQGB3hLAIBAK7I4RFIBDYHSEsAoHA7ghhEQgEdkcIi0AgsDtCWAQCgd0RwiIQCOxO... | <image>In \odot R, S U = 20, Y W = 20, and m \widehat Y X = 45. Find W Z. | A | 952 | null | A |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAUMAAADKCAYAAAA/+yKjAAAeFklEQVR4nO3de1yUddrH8Q9yEARBQUQFwQMiKrqgoiVs+rip1bpRdrSnNdvssKZ7qGzbfHZb97X2qnzttru2tdv6lOWT1baZdN7aTEoqz67iCVFT8TCOgBwEBIZ5/hgHRoRhBmZkDt/3X6PcM3Ojw5fffd/XfV0BZrPZjIiIn+vW1TsgIuIJFIYiIigMRUQAhaGICKAwFBEBFIYiIoDCUEQEUBiKiAAKQxERQGEoIgIoDEVEAIWhiAigMBQR... | <image>Find the measure of the altitude drawn to the hypotenuse. | D | 953 | null | D |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAVsAAAC8CAYAAADW+Q1jAAAYR0lEQVR4nO3d/1NU570H8Hfv9FdZMgzM1C+IE12+bPQmkRWhmTgKUaS2CfkisUZqtI5Gb6z13sSYxptJc1uNaSmjkehYE4e0N4p6SXtbJARwTC2Ii5qrLiimU1jR3AvDlMU/wPvD2XP2LLt79gDLOYfneb9mmFmXs+4znPP57LPP85zn860HDx48ABERTap/srsBREQyYLIlIrIAky0RkQWYbImILMBkS0RkASZbIiILMNkSEVmAyZaIyAJM... | <image>Parallelogram M N P Q is shown. What is the value of x? | A | 954 | null | A |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAegAAAEpCAYAAABY5LEdAAAmSElEQVR4nO3dT2wUV7r38ScjIhmJTGGkLCByx7ygu3IraEbolaY9QGaRCKN7k6VtMYJ3A2aYSEiveC05SJdFBslhcXlvLmM7K9BYtpcEZFvM4o1h3LNBMyLq1l1chRenLcICyXZDJFsaJO7CPuXT5er/9eecqu9HiuT2n3ZR7fSvnjrnPOetN2/evBEAAGCUn8V9AAAAYCcCGgAAAxHQAAAYiIAGAMBABDQAAAYioAEAMBABDQCAgQhoAAAM... | <image>Find y so that the quadrilateral is a parallelogram. | C | 955 | null | C |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAjcAAACYCAYAAAAY/ci8AAAn9UlEQVR4nO3deUBVZf7H8TcCKkQoIoLKoiIoqJSQYi5ppZW2WJo12TLWWE2LM5VjvyZbnBob09axtCZLx8pWNdszxzSXzAXclUVRxBUBRQQULvf3x5VCuXAvyN0On9dfejnn8ly4nPO55/me7+NlNpvNiIiIiBhEE1cPQERERKQhKdyIiIiIoSjciIiIiKEo3IiIiIihKNyIiIiIoSjciIiIiKEo3IiIiIihKNyIiIiIoSjciIiIiKEo3IiI... | <image>Find F B if S A and F B are altitudes and \triangle R S T \sim \triangle E F G. | B | 956 | null | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAASkAAACcCAYAAAAj6V3wAAABRGlDQ1BJQ0MgUHJvZmlsZQAAeJxjYGASSSwoyGFhYGDIzSspCnJ3UoiIjFJgf8LAzCAOhLoMConJxQWOAQE+QCUMMBoVfLvGwAiiL+uCzFotY9AkXFqv75vflF356eodTPUogCsltTgZSP8B4vTkgqISBgbGFCBbubykAMTuALJFioCOArLngNjpEPYGEDsJwj4CVhMS5Axk3wCyBZIzEoFmML4AsnWSkMTTkdhQe0GA18XVx0ch2NXI3NDS... | <image>Find the area of the triangle. Round to the nearest hundredth. | B | 957 | null | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAcsAAAFeCAYAAADqqTS3AAAsjElEQVR4nO3dXWwb573n8X/OyUUCtJmkRS7cLudIqZELg6y9CbwFQtUvxaI5omBHe0cKMuSeC4uK6212C5VYVkBdwBWgGt2mSWVRuYmFaEXeHdWGKLQXJy9H9EE3SNYpCV8UTZMOkeQiaJ1xAsQ4a6z2QpnRzPBl+DLDITnfDxDA4stwQon8zfM8/+d57tvd3d0VAADQ0N8FfQIAAPQ7whIAABeEJQAALghLAABcEJYAALggLAEAcEFYAgDg... | <image>Find m \angle D. | B | 958 | null | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAokAAAGcCAYAAAC1JDqUAACdGklEQVR4nOzddXyV5/nH8c9xiSsEtxBFIhQJUKh7V6Gd/Npt7VZdt/q6rbJ27VbZ1nVb3Vd3d4NCgsVdCE4g7sef5/z+OOEkQQMFIud6v168WgI5PIGc53zPfV/XdWu8Xq8XIYQQQggh+tAO9gUIIYQQQoihR0KiEEIIIYTYi4REIYQQQgixFwmJQgghhBBiLxIShRBCCCHEXiQkCiGEEEKIvUhIFEIIIYQQe5GQKIQQQggh9iIhUQghhBBC... | <image>What is the value of x if m \widehat N R = 62 and m \widehat N P = 108? | C | 959 | null | C |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAWkAAAFKCAYAAADfQ67WAAABRmlDQ1BJQ0MgUHJvZmlsZQAAeJxjYGASSSwoyGFhYGDIzSspCnJ3UoiIjFJgf8LAzMDHIMQgw8CdmFxc4BgQ4ANUwgCjUcG3awyMIPqyLsisy79j76nNu7c/WdpE/GtOzxpM9SiAKyW1OBlI/wHi9OSCohIGBsYUIFu5vKQAxO4AskWKgI4CsueA2OkQ9gYQOwnCPgJWExLkDGTfALIFkjMSgWYwvgCydZKQxNOR2FB7QYDXxdXHRyHY1cjc... | <image>In the figure, m \angle 1 = 123. Find the measure of \angle 4. | B | 960 | null | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAmAAAAE6CAYAAACxlu7cAAABRmlDQ1BJQ0MgUHJvZmlsZQAAeJxjYGASSSwoyGFhYGDIzSspCnJ3UoiIjFJgf8LAzCDIIMbAyKCXmFxc4BgQ4ANUwgCjUcG3a0B1QHBZF2SW9PLvlU2BmXz/GZa+d+u+ex1TPQrgSkktTgbSf4A4PbmgqISBgTEFyFYuLykAsTuAbJEioKOA7DkgdjqEvQHEToKwj4DVhAQ5A9k3gGyB5IxEoBmML4BsnSQk8XQkNtReEOB1cfXxUQh2NTI3... | <image>Find the measure of \angle 1 if m \angle D G F = 53 and m \angle A G C = 40. | B | 961 | null | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAb8AAAEGCAYAAAD11pvPAAAfE0lEQVR4nO3deVyVdaLH8Q8CKgiiuCSuoLgg4I6aS9LiVpk3nWtpqy0zN81p5pbVTKuVM+1NY1NT2i2zUcvU7GZlZVcntVBEU3FFURNJUZBFAQ+Hc/84isdkh3PO85zn+/5L4DzP61cHzvc8v/P7/h4/h8PhQERExEIaeHsAIiIinqbwExERy1H4iYiI5Sj8RETEchR+IiJiOQo/ERGxHIWfiIhYjsJPREQsR+EnIiKWo/ATLzrBmsdHEB0Z... | <image>Find the measure of the altitude drawn to the hypotenuse. | B | 962 | null | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAegAAAG1CAYAAAAyQGclAACbeUlEQVR4nOzdd3xc1Zn/8c+dXtV7l3vvvWDTW+gEkkA6oYWStpts381vN9lkk5DQCSGVQEgIvRqDce+9SrKt3ttoer+/P2Y0kgDjJlsj6Xm/Xrx2cdD1tTW633vOeZ5zFFVVVYQQQgiRVDRDfQNCCCGE+DgJaCGEECIJSUALIYQQSUgCWgghhEhCEtBCCCFEEpKAFkIIIZKQBLQQQgiRhCSghRBCiCQkAS2EEEIkIQloIYQQIglJQAshhBBJ... | <image>Find x. | B | 963 | null | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAUIAAAD1CAYAAAAlFfzlAAA9pklEQVR4nO2deVxUZRfHvyOigLiAIiEo+6agiWuiSYWpaa6VaYtZ2ltqpZm+vlppmWZqm1laaVqpZaapZaWSYYqaC4igyCoqRMi+yOIw3PePAYRhgGEZZoZ5vp+Pn8/gXebMzL2/+zznnOccmSRJEgKBQGDEtNK1AQKBQKBrhBAKBAKjRwihQCAweoQQCgQCo0cIoUAgMHqEEAoEAqNHCKFAIDB6hBAKBAKjRwihQCAweoQQCgQCo6e1rg3Q... | <image>Find m \angle G. | B | 964 | null | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAM8AAACmCAYAAAB9etvNAAAOuUlEQVR4nO3de1xUdcLH8c8Io4aoICKibUoi5kqWZVmrFqZPpmUpq7Zr9+xmW2ZRdntK0yzdUrd1H+1p19Rat7yVWor3NDF1vSylT7y8RSWKCigq4gXwPH+IpqQ4nJk5Z87M9/3PVAfO/BI//M78zpkzLsMwDESkyqrZPQARp1I8IiYpHhGTFI+ISYrHxwpcoylwjbZ7GGIBxSNikuIRMUnxiJikeERMUjwiJikeEZMUj4hJikfEJMUjYpLi... | <image>Find y. | D | 965 | null | D |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAkkAAAF8CAYAAADb3y+3AAAxK0lEQVR4nO3deXwU9eH/8XfchCOEQNCAIeEIJOFIgoRThSpa8a5UarWiqAit+i3aYqs9rN/a2tPWo4r6U7Fo9evFtyhatVq+LSqHcgUh4QokGAIBAoQjEGOy7O+PkL2YTfaY3Z3dfT0fjz4endndyQjMziszn5lJcjgcDgEAAMDDadFeAQAAACsikgAAAAwQSQAAAAaIJAAAAANEEgAAgAEiCQAAwACRBAAAYIBIAgAAMEAkAQAAGCCSAAAA... | <image>If P R \parallel K L, K N = 9, L N = 16, P M = 2 K P, find M L. | C | 966 | null | C |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAtEAAAFyCAYAAAAzqYbaAABdt0lEQVR4nO3dfVjT5f4H8DcBKYioECKCiAiIigYI+AAdPOazHiHNzMqnE9Yv09JTWkcrs9JSM0tJMy1NS1PLxMx8yiMJmqCAAsqTzyBOAgWBiQz3+wM2NtjGNjb29H5dV9fl/WX77sbcvp/vvft+31ZisVgMIiIiIiJS2yOG7gARERERkalhEU1EREREpCEW0UREREREGmIRTURERESkIRbRREREREQaYhFNRERERKQhFtFERERERBpiEU1E... | <image>If \frac { I J } { X J } = \frac { H J } { Y J }, m \angle W X J = 130 and m \angle W Z G = 20, find m \angle J H I. | B | 967 | null | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAfwAAAGJCAYAAABvvYFhAABBPUlEQVR4nO3dX0xUebsv+O+7N3tOMaNvATmcGTVgoT2cCVMg2rFNuhBwX0jE6aY6cwMed4SbFnXeLa3jJqFJpBPaDNuouDsi9sWAeQ3U1XTRHTX2xRaQ6kRNaykVcsLbKlQNemYzEapxBmY2Z5yLsopaa9X/WqvWv+8n6TTFn2KpUM96fs/v9zx/eP/+/XsQERGRof2V2hdAREREymPAJyIiMgEGfCIiIhNgwCciIjIBBnwiIiITYMAnIiIy... | <image>Use parallelogram to, find x. | A | 968 | null | A |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAmcAAAGRCAYAAAAgkRSIAADqAUlEQVR4nOz9Z5Bc553veX5Pem/Lew/vvSVBL4myLXZL6pbaybW59+5s7NzdiHmzGxs7MRsxd2Z2+t6WWuq+7WRaLe9FEiRBeO9dee8rvbdnX5xEASQMAbCAygL+nwgFu8mqrASqKs8/n/P8np+iqqqKEEIIIYQoC7rFfgJCCCGEEOImGc6EEEIIIcqIDGdCCCGEEGVEhjMhhBBCiDIiw5kQQgghRBmR4UwIIYQQoozIcCaEEEIIUUZkOBNC... | <image>Find m \angle 4. | C | 969 | null | C |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAWYAAAEHCAYAAACdjuzpAAAzDElEQVR4nO3deVRU9f/H8ScBKogLKKKCgArue4IimlYuqSWYiamZVrbZpt/cysr6+rMiNTHL6hvllnumVu5Waiopivs6LoAYIjkoIiPCOL8/kHHcmAFmuHeY9+Oczhlk5s67A7x4876fez9OBoPBgBBCCNV4QOkChBBC3E6CWQghVEaCWQghVEaCWQghVEaCWQghVEaCWQghVEaCWQghVEaCWQghVEaCWQghVEaCWQghVEaCWQghVEaCWQgh... | <image>Find A C. | C | 970 | null | C |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAPwAAADECAYAAAC7gkynAAArd0lEQVR4nO2deUBUVfvHPzAMIouyCiiyKCigZiRqkpX7vpulqZWaWVa2UZalVvrrdUvL3tSstNQW99cltVxQM9xwyQVUQERAkF1ZBhhm5vcH27AMDIgwy/n8Y83cO1yG+z3Puec8z/cxKcy7o0IgEBgFpo19AQKBoOEQghcIjAgheIHAiBCCFwiMCCF4gcCIEIIXCIwIIXiBwIgQghcIjAgheIHAiBCCFwiMCCF4gcCIEIIXCIwIIfhGRUHG... | <image>Find m \angle W. | B | 971 | null | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAkkAAAF8CAYAAADb3y+3AAAxK0lEQVR4nO3deXwU9eH/8XfchCOEQNCAIeEIJOFIgoRThSpa8a5UarWiqAit+i3aYqs9rN/a2tPWo4r6U7Fo9evFtyhatVq+LSqHcgUh4QokGAIBAoQjEGOy7O+PkL2YTfaY3Z3dfT0fjz4endndyQjMziszn5lJcjgcDgEAAMDDadFeAQAAACsikgAAAAwQSQAAAAaIJAAAAANEEgAAgAEiCQAAwACRBAAAYIBIAgAAMEAkAQAAGCCSAAAA... | <image>If P R \parallel K L, K N = 9, L N = 16, P M = 2 K P, find K M. | B | 972 | null | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAASkAAACcCAYAAAAj6V3wAAABRGlDQ1BJQ0MgUHJvZmlsZQAAeJxjYGASSSwoyGFhYGDIzSspCnJ3UoiIjFJgf8LAzCAOhLoMConJxQWOAQE+QCUMMBoVfLvGwAiiL+uCzFotY9AkXFqv75vflF356eodTPUogCsltTgZSP8B4vTkgqISBgbGFCBbubykAMTuALJFioCOArLngNjpEPYGEDsJwj4CVhMS5Axk3wCyBZIzEoFmML4AsnWSkMTTkdhQe0GA18XVx0ch2NXI3NDS... | <image>Find the perimeter of the triangle. Round to the nearest hundredth. | B | 973 | null | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAZ8AAAGmCAYAAACjl4nxAAA+0klEQVR4nO3df3AU550m8MdZsgt3oJG8Rd0ZkIwNR5VZjZHtcuA8MpJzZ1ySClu7OBVJi48fVzECb2wcjFWFiYO9RHcyJpbxAcJ7B6iiIOXW3pXNIZUhiQXWpIypEOGZk6tYE+QZAXXHHtII38Je2OX+EN109/TMdPf0dL/d/XyqUtGMZqS2kOaZ932/3/e94+bNmzdBRETkoG+4fQFERBQ8DB8iInIcw4eIiBzH8CEiIscxfIiIyHEMHyIi... | <image>Find b in the given parallelogram. | B | 974 | null | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAb4AAAESCAYAAACCU7B8AABIw0lEQVR4nO3deVRTZ94H8C8FKlFECWJUUJBN1OBWwAVanI7WpR1xGWt1qtUp2mWw1bfFcaoz1hmxVmqtlW7Wjq1Ota2Vgrbu00oLdQEFNSqyo0GNkSAIBoZQ3j9ibhJIQgJJ7s3N73OO5yR6CY+Q3O+zPy4tLS0tIIQQQpzEQ2wXgBBCCLEnCj5CCCFOhYKPEEKIU6HgI4QQ4lQo+AghhDgVCj5CCCFOhYKPEEKIU6HgI4QQ4lQo+AghhDgV... | <image>The diameters of \odot A, \odot B, and \odot C are 10, 30 and 10 units, respectively. Find B Y if A Z \cong C W and C W = 2. | B | 975 | null | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAOgAAADLCAYAAABkkd/gAAABRmlDQ1BJQ0MgUHJvZmlsZQAAeJxjYGASSSwoyGFhYGDIzSspCnJ3UoiIjFJgf8LAzCDGIM6gz2CQmFxc4BgQ4ANUwgCjUcG3awyMIPqyLsgs+VNVf877TN/6iLfO3WPuVBNM9SiAKyW1OBlI/wHi9OSCohIGBsYUIFu5vKQAxO4AskWKgI4CsueA2OkQ9gYQOwnCPgJWExLkDGTfALIFkjMSgWYwvgCydZKQxNOR2FB7QYDXxdXHRyHY1cjc... | <image>Find the area of the figure. Round to the nearest tenth if necessary. | C | 976 | null | C |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAmcAAAGRCAYAAAAgkRSIAADqAUlEQVR4nOz9Z5Bc553veX5Pem/Lew/vvSVBL4myLXZL6pbaybW59+5s7NzdiHmzGxs7MRsxd2Z2+t6WWuq+7WRaLe9FEiRBeO9dee8rvbdnX5xEASQMAbCAygL+nwgFu8mqrASqKs8/n/P8np+iqqqKEEIIIYQoC7rFfgJCCCGEEOImGc6EEEIIIcqIDGdCCCGEEGVEhjMhhBBCiDIiw5kQQgghRBmR4UwIIYQQoozIcCaEEEIIUUZkOBNC... | <image>Find m \angle 7. | C | 977 | null | C |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAO4AAADvCAYAAAD1suiHAAAzNklEQVR4nO2de1xUdf7/nywglxAERURHLnIRELygoAlettXSbt6yNncr3azd0tp1W/25WWnb2teystKtrWhNK90yb1mp6ZaWmhcEFURBQEQQEQG5yEUY5/fHMMMMDsMAczln+DwfDx+P43AO82HmvM7n/Xl/3hcHlUqlQiAQyIpf2XoAAoGg/QjhCgQyRAhXIJAhQrgCgQwRwhUIZIgQrkAgQ4RwBQIZIoQrEMgQIVyBQIYI4QoEMkQIVyCQ... | <image>Rhombus A B C D is circumscribed about \odot P and has a perimeter of 32. Find x. | C | 978 | null | C |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAjkAAAF/CAYAAACrAtiBAABiE0lEQVR4nO3dd5xU9b3/8deZPjvbe6XvLioWBEEQe++KJsaYYro1JjfJzS83uTfl5qZ3a6LGVI1G7BqNvSAiKCoibAG2916mz5zfHzM7ix12F3aZeT8fyT95wGYYmHPe8zmf7+djmKZpIiIiIpJkLNP9AkRERET2BoUcERERSUoKOSIiIpKUFHJEREQkKSnkiIiISFJSyBEREZGkpJAjIiIiSUkhR0RERJKSQo6IiIgkJYUcERERSUoKOSIi... | <image>If A C = 14, B C = 8, and A D = 21, find E D. | B | 979 | null | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAuIAAAILCAYAAACtqPl1AAEAAElEQVR4nOz9d3Rc93nv/7739D6YGWAGHSBBAuwUJXb1LstxTdzj3pKc5OTkOKese9dd69z7u+t3T3pyck7iuNux4zhOXGOrS6Qau0RRFIlGEh2YAQbT+8ze9489GIISqwQSAPG81nKcBYPAkAAGn/nuz34eRdM0DSGEEEIIIcQNZVjsByCEEEIIIcRKJEFcCCGEEEKIRSBBXAghhBBCiEUgQVwIIYQQQohFIEFcCCGEEEKIRSBBXAghhBBC... | <image>R P = 3.5 and J P = 9. Find P L. | C | 980 | null | C |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAVcAAAEWCAYAAADSNdTRAAABRGlDQ1BJQ0MgUHJvZmlsZQAAeJxjYGASSSwoyGFhYGDIzSspCnJ3UoiIjFJgf8LAzCAKhLwMyonJxQWOAQE+QCUMMBoVfLvGwAiiL+uCzOKK+Han7EqwsuVDi8OzwwVXYqpHAVwpqcXJQPoPEKcnFxSVMDAwpgDZyuUlBSB2B5AtUgR0FJA9B8ROh7A3gNhJEPYRsJqQIGcg+waQLZCckQg0g/EFkK2ThCSejsSG2gsCvC6uPj4Kwa5G5oaW... | <image>In the figure, the vertices of quadrilateral A B C D intersect square E F G H and divide its sides into segments with measure that have a ratio of 1:2. Find the area of A B C D. | B | 981 | null | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAbMAAADbCAYAAADnPX8EAABLEElEQVR4nO2dd1hUR9uH72UBBUTpIKhBRFTAjg1FIoomFuxGXzUx+hqNRlMsMcWU15io0RSTqCmaWBKNLZ+KRKNBjcTeFeyKIr0qAlKW/f6AxQV2qbuwu8x9XbmCp845Z/b8zsz85nkkmRnRcgQCgUAg0GOMarsAAoFAIBBUF2OpRFLbZRAIBAKBoFoYCy0TCAQCgb5jDELNBAKBQKDfGBsZiWEzgUAgEOg3QskEAoFAoPcIMRMIBAKB3iPE... | <image>Quadrilateral A B C D is a rectangle. Find y. | A | 982 | null | A |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAARMAAAD6CAYAAACClaNGAAAo9UlEQVR4nO3de1yUdfr/8RcgKQKCgIigiCCKiHlCU1LM1N3VWlvL2tx0SytrdX9Wrlu2fbez28lOftdsza9W2sk0dzuYJWq6iZWKloooQpxBhZHzMAIzvz+mGQY5DTDDzNz39Xw8fDwAB705zHs+93197utyq6spMCCEEJ3k7ugDEEIog4SJEMImJEyEEDYhYSKEsAkJEyGETUiYCCFsQsJECGETEiZCCJuQMBFC2ISEiRDCJiRMhBA2IWEi... | <image>Find the perimeter of \triangle Q R S if \triangle Q R S \sim \triangle Q T P. | B | 983 | null | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAOgAAACOCAYAAAA7BEQ/AAAbG0lEQVR4nO2deUAT1/bHv9QoBANKEKMCimyCjVqQRQuKr9W61CeoVZ9rnxW7aav+WqyttthFa2t9tmqtVaxrsWql1b5KRdqnFYqyKCourIIElYYEiGBAgvz+iAmTECCQZWaS+/krJDOTQ2a+99xz7rn32jQ1NTWBQCAwkifoNoBAILQOESiBwGCIQAkEBkMESiAwGCJQAoHBEIESCAyGCJRAYDBEoAQCgyECJRAYDBEogcBgiEAJBAZDBEog... | <image>Find x. Assume that any segment that appears to be tangent is tangent. | D | 984 | null | D |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAATkAAADmCAYAAACu/vK/AAAbKElEQVR4nO3de3iU5bnv8W+cxBASjiEGJJyRY9BwCpSEohZP1IUtHtaiB1BLtxXBbnVjrXRptVvLlrZWpXjtvdhF7epyWxQLRSvgCRtUEiAgIYEEwimAISRqGEggmcz+Iw4dhkkyk8zMe/p9ros/gAl5Apkf7/2+z30/cV6v14uIiE1dYvQCRESiSSEnIramkBMRW1PIiYitKeRExNYUciJiawo5EbE1hZyI2JpCTkRsTSEnIramkBMRW1PI... | <image>If P T = y - 3, P S = y + 2, R S = 12, and Q S = 16 solve for y. | D | 985 | null | D |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAacAAADhCAYAAABsmXpdAAA21ElEQVR4nO3deUCU1frA8S8CsoRsLqiAoCCg4oKKmmBQuZaJStbVyuVme3bzFlxvVmpdu6aV3Sy7FUVWP8trLmiLW6UmargrhiIoIKiIgCACCuP8/sBBkG2AWd4Zns9fOrzvzJnh5X3mnOec81io1Wo1QgghhIK0MnYDhBBCiNtJcBJCCKE4EpyEEEIojgQnIYQQiiPBSQghhOJIcBJCCKE4EpyEEEIojgQnIYQQiiPBSQghhOJIcBJCCKE4... | <image>Find A B. | C | 986 | null | C |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAegAAAHPCAYAAACY+UmCAACbSUlEQVR4nOzddWBbV5r38e8Vy5YsycwYh5mZqczcpkkKM4XpTAcW3t2d2dmBndnpQCdQDjRpysxtmJnZzGzZki2W7vuHZCelcGzZPp//mlrysS3dn8655zyPJMuyjCAIgiAIYUXR2QMQBEEQBOG7REALgiAIQhgSAS0IgiAIYUgEtCAIgiCEIRHQgiAIghCGREALgiAIQhgSAS0IgiAIYUgEtCAIgiCEIRHQgiAIghCGREALgiAIQhgSAS0I... | <image>Find D F. | A | 987 | null | A |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAQ8AAADNCAYAAACmePU1AAABRmlDQ1BJQ0MgUHJvZmlsZQAAeJxjYGASSSwoyGFhYGDIzSspCnJ3UoiIjFJgf8LAzCDOwM8gyyCcmFxc4BgQ4ANUwgCjUcG3awyMIPqyLsis6bce3FrtZzyDZVvGAdHJ7DMw1aMArpTU4mQg/QeI05MLikoYGBhTgGzl8pICELsDyBYpAjoKyJ4DYqdD2BtA7CQI+whYTUiQM5B9A8gWSM5IBJrB+ALI1klCEk9HYkPtBQFeF1cfH4VgVyNz... | <image>Find x. | D | 988 | null | D |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAcsAAAFeCAYAAADqqTS3AAAsjElEQVR4nO3dXWwb573n8X/OyUUCtJmkRS7cLudIqZELg6y9CbwFQtUvxaI5omBHe0cKMuSeC4uK6212C5VYVkBdwBWgGt2mSWVRuYmFaEXeHdWGKLQXJy9H9EE3SNYpCV8UTZMOkeQiaJ1xAsQ4a6z2QpnRzPBl+DLDITnfDxDA4stwQon8zfM8/+d57tvd3d0VAADQ0N8FfQIAAPQ7whIAABeEJQAALghLAABcEJYAALggLAEAcEFYAgDg... | <image>Find m \angle A. | B | 989 | null | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAUwAAADCCAYAAAAio/tDAAApzUlEQVR4nO2df1BUZ5rvvxiM4CgHnJgETbegjnOL6o6Mrjs30wQ1d0sLmERm61YtUGTBfwJqcofZWZcqQ5WkiljFuNklV9HGf4I1FvRUzU4wGZrSqomAdKYybFy0u6wbZ0A8HSWJWZuDTsCEmPtH93s4/ePQTff51d3PpypVnT50nxdpvjzv83zf58n47rvvvgNBEAQRlWV6L4AgCCJZIMEkCIKIERJMgiCIGCHBJAiCiBESTIIgiBghwSQI... | <image>Find x so that the quadrilateral is a parallelogram. | A | 990 | null | A |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAgQAAAG/CAYAAAAn58+9AACesklEQVR4nOzdd3xV9fnA8c+5++Zm70EWAZIwBBTcEweIWxnWVbfWn62j1Wq1Vltb6657a9U6EcWBijhREQHZZAAJZO95b3L3Ob8/Eu5NEJQRkpvkeb9evmwVYyTnnvOc5/sMRdM0DSGEEEIMa7qB/gaEEEIIMfAkIBBCCCGEBARCCCGEkIBACCGEEEhAIIQQQggkIBBCCCEEEhAIIYQQAgkIhBBCCIEEBEIIIYRAAgIhhBBCIAGBEEIIIZCA... | <image>Find x. | B | 991 | null | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAY4AAAEACAYAAACkvpHUAAABRmlDQ1BJQ0MgUHJvZmlsZQAAeJxjYGASSSwoyGFhYGDIzSspCnJ3UoiIjFJgf8LAzCDNwMvAxcCWmFxc4BgQ4ANUwgCjUcG3awyMIPqyLsgsobSDM7jnPHqnzpEXkd/omY2pHgVwpaQWJwPpP0CcnlxQVMLAwJgCZCuXlxSA2B1AtkgR0FFA9hwQOx3C3gBiJ0HYR8BqQoKcgewbQLZAckYi0AzGF0C2ThKSeDoSG2ovCPC6uPr4KAS7Gpkb... | <image>P Q is tangent to the circle. Find x. Round to the nearest tenth. | B | 992 | null | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAaUAAAFlCAYAAABLOvcaAAABRmlDQ1BJQ0MgUHJvZmlsZQAAeJxjYGASSSwoyGFhYGDIzSspCnJ3UoiIjFJgf8LAzCDOIMxgxKCQmFxc4BgQ4ANUwgCjUcG3awyMIPqyLsisy9KZZ1r+/9V1aWsTOvyc7xmmehTAlZJanAyk/wBxenJBUQkDA2MKkK1cXlIAYncA2SJFQEcB2XNA7HQIewOInQRhHwGrCQlyBrJvANkCyRmJQDMYXwDZOklI4ulIbKi9IMDr4urjoxDsamRu... | <image>In the figure, below, square A B C D is attached to \triangle A D E as shown. If m \angle E A D is 30 and A E is equal to 4 \sqrt { 3 }, then what is the area of square A B C D? | C | 993 | null | C |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAARAAAACrCAYAAACucMMXAAASAUlEQVR4nO3deVgUZ54H8C8RVJCgYBJGESEcXiExGlH38cwoJhrjmUtz6KxM1iSa9RgybIxXMk40RuPGI5mNCZoYsxPHAzPR0cFdVNCsiALiwaWIjQaRG2wau639Aynpphu6i+6q6ub7eR4fG6pL31fg61vvW/X+3ARBEEBEJMEDSjeAiJwXA4SIJGOAEJFkDBAikowBQkSSMUCISDIGCBFJxgAhIskYIEQkGQOEiCRjgKjYnqR8pZtA1CwG... | <image>Find x. | A | 994 | null | A |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAegAAAEpCAYAAABY5LEdAAAmSElEQVR4nO3dT2wUV7r38ScjIhmJTGGkLCByx7ygu3IraEbolaY9QGaRCKN7k6VtMYJ3A2aYSEiveC05SJdFBslhcXlvLmM7K9BYtpcEZFvM4o1h3LNBMyLq1l1chRenLcICyXZDJFsaJO7CPuXT5er/9eecqu9HiuT2n3ZR7fSvnjrnPOetN2/evBEAAGCUn8V9AAAAYCcCGgAAAxHQAAAYiIAGAMBABDQAAAYioAEAMBABDQCAgQhoAAAM... | <image>Find x so that the quadrilateral is a parallelogram. | B | 995 | null | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAi8AAAFDCAYAAADyCu74AAAr10lEQVR4nO3db2wb953n8a+7voONbTK2u8EhzZF17cIPcuTF2CLAwcPKyfYAQ9LZ0UNJ68LpE4vaXLsKCleA6gcK4DWgGD0o6fpEBQesjQgiH9otLCEGisYO6cMh6KEBiT4w6j8Z4pIDgo08ueKiA7zQPZBnPBySoxlyOH/fr0eSTFETRdJ8+f39fp/vrq2trS0BAACIiW+EfQEAAABeULwAAIBYoXgBAACxQvECAABiheIFAADECsULAACI... | <image>Quadrilateral A B D C is a rectangle. Find m \angle 5 if m \angle 1 = 38. | C | 996 | null | C |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAuIAAAILCAYAAACtqPl1AAEAAElEQVR4nOz9d3Rc93nv/7739D6YGWAGHSBBAuwUJXb1LstxTdzj3pKc5OTkOKese9dd69z7u+t3T3pyck7iuNux4zhOXGOrS6Qau0RRFIlGEh2YAQbT+8ze9489GIISqwQSAPG81nKcBYPAkAAGn/nuz34eRdM0DSGEEEIIIcQNZVjsByCEEEIIIcRKJEFcCCGEEEKIRSBBXAghhBBCiEUgQVwIIYQQQohFIEFcCCGEEEKIRSBBXAghhBBC... | <image>R P = 3.5 and J P = 9. Find P S. | B | 997 | null | B |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAhYAAAFnCAYAAAD60QAqAAB8aElEQVR4nO3dd3xV9f348de5e2Xd3CRAWAk7YQkoioADQWS6625rd+34do9fh927tmrtssPW0VpbZQoioICAKCBCEvZICGTc7LvPPef8/rgBAiSQQHbez8ejf7QFciG5977uZyqGYRgIIYQQQrQDU1c/ACGEEEL0HhIWQgghhGg3EhZCCCGEaDcSFkIIIYRoNxIWQgghhGg3EhZCCCGEaDcSFkIIIYRoNxIWQgghhGg3EhZCCCGEaDcSFkII... | <image>Find x. | C | 998 | null | C |
[
{
"bytes": "iVBORw0KGgoAAAANSUhEUgAAAlcAAAF5CAYAAACydQ9fAABUwElEQVR4nO3df2xTd94v+Hd3uav0qnCaalmJUrtJQWjL2pCnXabPrdMERrdUcQTxc2euJsnNKKFXD3GaoU2nw2SVh1voiGGVMr1Nh0mT9O5AoubGfjR0rgElEfTZp0Dj7vRBnQnYSiVUfvSYFGmRSE7SfRLpiS77hzkn5xz/to/tY/v9kirhg33yjYuPP+f7/Xw/n0cePHjwAERERERkiP8h3wMgIiIiKiYMroiIiIgMxOCKiIiIyEAMroiI... | <image>Find m \angle C. | D | 999 | null | D |
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