{"id":"cb_question_bank:16b8a398-2d02-400e-b5e3-f1270f5a9c35","source_id":"cb_question_bank","source_item_id":"16b8a398-2d02-400e-b5e3-f1270f5a9c35","external_id":"dbae1ccb-c727-453d-aad3-d9808097dcfd","ibn":null,"question_id":"d5f349b7","program":"SAT","module":"math","domain_code":"S","domain":"Geometry and Trigonometry","skill_code":"S.B.","skill":"Lines, angles, and triangles","difficulty":"E","score_band":3,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"Right triangle upper P upper Q upper R is labeled as follows: Angle upper R is a right angle. Right triangle upper S upper T upper U is labeled as follows: Angle upper U is a right angle. A note indicates the figures are not drawn to scale. Right triangles upper P upper Q upper R and upper S upper T upper U are similar, where upper P corresponds to upper S . If the measure of angle upper Q is 18 degree , what is the measure of angle upper S ?","stimulus":"","stimulus_html":null,"stem_html":"

\n

Right triangles \n\tP\n\tQ\n\tR\n\n and \n\tS\n\tT\n\tU\n\n are similar, where P\n corresponds to S\n. If the measure of angle Q\n is 18°, what is the measure of angle S\n?

","rationale_html":"

Choice B is correct. In similar triangles, corresponding angles are congruent. It’s given that right triangles \n\tP\n\tQ\n\tR\n\n and \n\tS\n\tT\n\tU\n\n are similar, where angle P\n corresponds to angle S\n. It follows that angle P\n is congruent to angle S\n. In the triangles shown, angle R\n and angle U\n are both marked as right angles, so angle R\n and angle U\n are corresponding angles. It follows that angle Q\n and angle T\n are corresponding angles, and thus, angle Q\n is congruent to angle T\n. It’s given that the measure of angle Q\n is 18°, so the measure of angle T\n is also 18°. Angle U\n is a right angle, so the measure of angle U\n is 90°. The sum of the measures of the interior angles of a triangle is 180°. Thus, the sum of the measures of the interior angles of triangle \n\tS\n\tT\n\tU\n\n is 180\n degrees. Let s\n represent the measure, in degrees, of angle S\n. It follows that s+18+90=180, or \n\t\n\t\ts\n\t\t+\n\t\t108\n\t\n\t=\n\t180\n\n. Subtracting 108\n from both sides of this equation yields \n\ts\n\t=\n\t72\n\n. Therefore, if the measure of angle Q\n is 18\n degrees, then the measure of angle S\n is 72\n degrees.

\n

Choice A is incorrect. This is the measure of angle T\n.

\n

Choice C is incorrect and may result from conceptual or calculation errors.

\n

Choice D is incorrect. This is the sum of the measures of angle S\n and angle U\n.

","correct_answer":["B"],"has_media":true,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.837000+00:00","source_updated_at":"2023-08-02T20:25:59.837000+00:00","options":[{"label":"A","content_html":"

18°

","ord":0},{"label":"B","content_html":"

72°

","ord":1},{"label":"C","content_html":"

82°

","ord":2},{"label":"D","content_html":"

162°

","ord":3}],"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}}