{"id":"cb_question_bank:12afd426-90e4-4d60-abc3-1d75c8f272e3","source_id":"cb_question_bank","source_item_id":"12afd426-90e4-4d60-abc3-1d75c8f272e3","external_id":null,"ibn":"05757-DC","question_id":"947a3cde","program":"SAT","module":"math","domain_code":"S","domain":"Geometry and Trigonometry","skill_code":"S.B.","skill":"Lines, angles, and triangles","difficulty":"H","score_band":6,"answer_type":"spr","answer_source":"rationale","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"In the figure above, line segment M Q and line segment N R intersect at point P , N P equals Q P , and M P equals P R . What is the measure, in degrees, of angle Q M R ? (Disregard the degree symbol when gridding your answer.)","stimulus":"The figure presents line segments MQ and NR that intersect at point P, where point N is above and slightly to the right of point M and point Q is above and slightly to the left of point R. Line segments MN, QR, and horizontal line segment M, R are drawn forming triangles MNR and QMR. The measure of angle QPR is labeled 60 degrees and the angle measure of MQR is labeled 70 degrees.","stimulus_html":"
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In the figure above, \"line and \"line intersect at point P, \"N, and \"M. What is the measure, in degrees, of \"angle ? (Disregard the degree symbol when gridding your answer.)

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The correct answer is 30. It is given that the measure of \"angle is \"60. Angle MPR and \"angle are collinear and therefore are supplementary angles. This means that the sum of the two angle measures is \"180, and so the measure of \"angle is \"120. The sum of the angles in a triangle is \"180. Subtracting the measure of \"angle from \"180 yields the sum of the other angles in the triangle MPR. Since \"180, the sum of the measures of \"angle and \"angle is \"60. It is given that \"the, so it follows that triangle MPR is isosceles. Therefore\"angle and \"angle must be congruent. Since the sum of the measure of these two angles is \"60, it follows that the measure of each angle is \"30.

An alternate approach would be to use the exterior angle theorem, noting that the measure of \"angle is equal to the sum of the measures of \"angle and \"angle. Since both angles are equal, each of them has a measure of \"30.

\n","correct_answer":["30"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.630000+00:00","source_updated_at":"2023-08-02T20:25:59.630000+00:00","options":[],"attribution":{"source_id":"cb_question_bank","source_name":"College Board digital SAT question bank (community dump)","rights_holder":"College Board","canonical_url":"https://satsuitequestionbank.collegeboard.org/","retrieved_from":"https://raw.githubusercontent.com/mdn522/sat-question-bank/main/data/cb-digital-questions.json","attribution":"SAT practice questions © College Board, from the official SAT Suite Question Bank. Retrieved via the community dump at github.com/mdn522/sat-question-bank.","disclaimer":"SAT® and PSAT/NMSQT® are trademarks registered by the College Board, which is not affiliated with, does not sponsor, and does not endorse this project.","license":"College Board copyright; source repository carries no licence. Local use only.","redistributable":false,"item_count":2017}}