{"id":"cb_question_bank:cb66a88f-0478-41b6-b07b-50bd2384995a","source_id":"cb_question_bank","source_item_id":"cb66a88f-0478-41b6-b07b-50bd2384995a","external_id":"33267cea-2b74-4c39-98b4-c53cd17a378d","ibn":null,"question_id":"17912810","program":"SAT","module":"math","domain_code":"S","domain":"Geometry and Trigonometry","skill_code":"S.B.","skill":"Lines, angles, and triangles","difficulty":"H","score_band":7,"answer_type":"spr","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"Counterclockwise from top right, the lines are labeled s, r, q, and t. Line s intersects line r above line q. Line s and line r each intersect line q and line t. At the intersection of line s and line r, 1 angle is labeled counterclockwise from top as follows: Top: a° At the intersection of line s and line q, 1 angle is labeled counterclockwise from top-left as follows: Top left: b° At the intersection of line r and line t: The line segment divides the bottom-left angle into two equal angles, each labeled w°. A note indicates the figure is not drawn to scale. In the figure, parallel lines q and t are intersected by lines r and s . If a equals 43 and b equals 122 , what is the value of w ?","stimulus":"","stimulus_html":null,"stem_html":"

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In the figure, parallel lines q\n and t\n are intersected by lines r\n and s\n. If \n\ta\n\t=\n\t43\n\n and \n\tb\n\t=\n\t122\n\n, what is the value of w\n?

","rationale_html":"

The correct answer is \n\t101\n\t2\n\n. In the figure, lines q\n, r\n, and s\n form a triangle. One interior angle of this triangle is vertical to the angle marked a°; therefore, the interior angle also has measure a°. It's given that \n\ta\n\t=\n\t43\n\n. Therefore, the interior angle of the triangle has measure 43°. A second interior angle of the triangle forms a straight line, q\n, with the angle marked b°. Therefore, the sum of the measures of these two angles is 180°. It's given that \n\tb\n\t=\n\t122\n\n. Therefore, the angle marked b° has measure 122° and the second interior angle of the triangle has measure 180-122°, or 58°. The sum of the interior angles of a triangle is 180°. Therefore, the measure of the third interior angle of the triangle is 180-43-58°, or 79°. It's given that parallel lines q\n and t\n are intersected by line r\n. It follows that the triangle's interior angle with measure 79° is congruent to the same side interior angle between lines q\n and t\n formed by lines t\n and r\n. Since this angle is supplementary to the two angles marked w°, the sum of 79°, w°, and w° is 180°. It follows that 79+w+w=180, or 79+2w=180. Subtracting 79\n from both sides of this equation yields 2w=101. Dividing both sides of this equation by 2\n yields \n\tw\n\t=\n\t\n\t\t101\n\t\t2\n\t\n\n. Note that 101/2 and 50.5 are examples of ways to enter a correct answer.

","correct_answer":["101/2","50.5"],"has_media":true,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.840000+00:00","source_updated_at":"2023-08-02T20:25:59.840000+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}}