{"id":"cb_question_bank:19073eba-8dbd-4a20-8045-b61f18ee98ad","source_id":"cb_question_bank","source_item_id":"19073eba-8dbd-4a20-8045-b61f18ee98ad","external_id":"c39deac6-0f67-4431-b530-e4745624b358","ibn":null,"question_id":"686b5212","program":"SAT","module":"math","domain_code":"S","domain":"Geometry and Trigonometry","skill_code":"S.B.","skill":"Lines, angles, and triangles","difficulty":"M","score_band":5,"answer_type":"spr","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"Clockwise from top left, the 3 lines are labeled s, q, and r. Line s intersects both line q and line r. At the intersection of line s and line q, 1 angle is labeled clockwise from top left as follows: Top right: 58° At the intersection of line s and line r, 1 angle is labeled clockwise from top left as follows: Top left: y° A note indicates the figure is not drawn to scale. In the figure, line q is parallel to line r , and both lines are intersected by line s . If y equals 2 x plus 8 , what is the value of x ?","stimulus":"","stimulus_html":null,"stem_html":"

\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n\n

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In the figure, line q\n is parallel to line r\n, and both lines are intersected by line s\n. If \n\ty\n\t=\n\t\n\t\t\n\t\t\t2\n\t\t\tx\n\t\t\n\t\t+\n\t\t8\n\t\n\n, what is the value of x\n?

","rationale_html":"

The correct answer is 57\n. Based on the figure, the angle with measure y° and the angle vertical to the angle with measure 58° are same side interior angles. Since vertical angles are congruent, the angle vertical to the angle with measure 58° also has measure 58°. It’s given that lines q\n and r\n are parallel. Therefore, same side interior angles between lines q\n and r\n are supplementary. It follows that \n\t\n\t\ty\n\t\t+\n\t\t58\n\t\n\t=\n\t180\n\n. If \n\ty\n\t=\n\t\n\t\t\n\t\t\t2\n\t\t\tx\n\t\t\n\t\t+\n\t\t8\n\t\n\n, then the value of x\n can be found by substituting \n\t\n\t\t2\n\t\tx\n\t\n\t+\n\t8\n\n for y\n in the equation \n\t\n\t\ty\n\t\t+\n\t\t58\n\t\n\t=\n\t180\n\n, which yields 2x+8+58=180, or 2x+66=180. Subtracting 66\n from both sides of this equation yields \n\t\n\t\t2\n\t\tx\n\t\n\t=\n\t114\n\n. Dividing both sides of this equation by 2\n yields \n\tx\n\t=\n\t57\n\n. Thus, if \n\ty\n\t=\n\t\n\t\t\n\t\t\t2\n\t\t\tx\n\t\t\n\t\t+\n\t\t8\n\t\n\n, the value of x\n is 57\n.

","correct_answer":["57"],"has_media":true,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.838000+00:00","source_updated_at":"2023-08-02T20:25:59.838000+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}}