{"id":"cb_practice_pdf:t4-math-m1-q9","source_id":"cb_practice_pdf","source_item_id":"t4-math-m1-q9","external_id":null,"ibn":null,"question_id":null,"program":"SAT","module":"math","domain_code":null,"domain":null,"skill_code":null,"skill":null,"difficulty":null,"score_band":null,"answer_type":"mcq","answer_source":"rationale","layout_warning":null,"form_id":"cb_practice_pdf:test-4","module_number":1,"position":9,"stem":"Q S~: P ___....._.R Note: Figures not drawn to scale. Right triangles PQR and STU are similar, where P corresponds to S. If the measure of angle Q is 18°, what is the measure of angle S?","stimulus":"","stimulus_html":null,"stem_html":"<p>Q S~: P ___....._.R Note: Figures not drawn to scale. Right triangles PQR and STU are similar, where P corresponds to S. If the measure of angle Q is 18°, what is the measure of angle S?</p>","rationale_html":"<p>Choice B is correct. In similar triangles, corresponding angles are congruent. It’s given that right triangles PQR and STU are similar, where angle P corresponds to angle S. It follows that angle P is congruent to angle S. In the triangles shown, angle R and angle U are both marked as right angles, so angle R and angle U are corresponding angles. It follows that angle Q and angle T are corresponding angles, and thus, angle Q is congruent to angle T. It’s given that the measure of o o angle Q is 18 , so the measure of angle T is also 18 . Angle U is a right angle, o so the measure of angle U is 90 . The sum of the measures of the interior angles o of a triangle is 180 . Thus, the sum of the measures of the interior angles of triangle STU is 180 degrees. Let s represent the measure, in degrees, of angle + + = + = S. It follows that s 18 90 180, or s 108 180. Subtracting 108 from both = sides of this equation yields s 72. Therefore, if the measure of angle Q is 18 degrees, then the measure of angle S is 72 degrees. Choice A is incorrect. This is the measure of angle T. Choice C is incorrect and may result from conceptual or calculation errors. Choice D is incorrect. This is the sum of the measures of angle S and angle U.</p>","correct_answer":["B"],"has_media":false,"has_mathml":false,"has_table":false,"source_created_at":null,"source_updated_at":null,"options":[{"label":"A","content_html":"<p>18°</p>","ord":0},{"label":"B","content_html":"<p>72°</p>","ord":1},{"label":"C","content_html":"<p>82°</p>","ord":2},{"label":"D","content_html":"<p>162°</p>","ord":3}],"attribution":{"source_id":"cb_practice_pdf","source_name":"College Board full-length SAT practice tests (PDF)","rights_holder":"College Board","canonical_url":"https://satsuite.collegeboard.org/practice/practice-tests/paper","retrieved_from":"https://satsuite.collegeboard.org/practice/practice-tests/paper","attribution":"Full-length SAT practice tests 4–11 © College Board, published free at satsuite.collegeboard.org.","disclaimer":"Extracted from PDF layout: equations, figures and tables do not survive intact. Use the original PDFs for anything the text renders poorly. SAT® is a trademark registered by the College Board, which is not affiliated with and does not endorse this project.","license":"College Board copyright. Free to download; not licensed for redistribution.","redistributable":false,"item_count":905}}