{"id":"cb_question_bank:52b4079a-9403-4b02-8918-d369a825a666","source_id":"cb_question_bank","source_item_id":"52b4079a-9403-4b02-8918-d369a825a666","external_id":"4e338dff-7649-48c0-89f7-665b5a7d5776","ibn":null,"question_id":"3b225698","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":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"Triangle upper X upper Y upper Z is similar to triangle upper R upper S upper T such that upper X , upper Y , and upper Z correspond to upper R , upper S , and upper T , respectively. The measure of angle upper Z is 20 degree and 2 upper X upper Y equals upper R upper S . What is the measure of angle upper T ?","stimulus":"","stimulus_html":null,"stem_html":"<p>Triangle <math alttext=\"upper X upper Y upper Z\"><mrow>\n\t<mi>X</mi>\n\t<mi>Y</mi>\n\t<mi>Z</mi>\n</mrow>\n</math> is similar to triangle <math alttext=\"upper R upper S upper T\"><mrow>\n\t<mi>R</mi>\n\t<mi>S</mi>\n\t<mi>T</mi>\n</mrow>\n</math> such that <math alttext=\"upper X\"><mi>X</mi>\n</math>, <math alttext=\"upper Y\"><mi>Y</mi>\n</math>, and <math alttext=\"upper Z\"><mi>Z</mi>\n</math> correspond to <math alttext=\"upper R\"><mi>R</mi>\n</math>, <math alttext=\"upper S\"><mi>S</mi>\n</math>, and <math alttext=\"upper T\"><mi>T</mi>\n</math>, respectively. The measure of <math alttext=\"angle upper Z\"><mo>∠</mo><mi>Z</mi></math> is <math alttext=\"20 degree\"><mn>20</mn>\n<mo>°</mo></math> and <math alttext=\"2 upper X upper Y equals upper R upper S\"><mrow>\n\t<mrow>\n\t\t<mn>2</mn>\n\t\t<mi>X</mi>\n\t\t<mi>Y</mi>\n\t</mrow>\n\t<mo>=</mo>\n\t<mrow>\n\t\t<mi>R</mi>\n\t\t<mi>S</mi>\n\t</mrow>\n</mrow>\n</math>. What is the measure of <math alttext=\"angle upper T\"><mo>∠</mo><mi>T</mi></math>?</p>","rationale_html":"<p style=\"text-align: left;\">Choice C is correct. It’s given that triangle <math alttext=\"upper X upper Y upper Z\"><mrow>\n\t<mi>X</mi>\n\t<mi>Y</mi>\n\t<mi>Z</mi>\n</mrow>\n</math> is similar to triangle <math alttext=\"upper R upper S upper T\"><mrow>\n\t<mi>R</mi>\n\t<mi>S</mi>\n\t<mi>T</mi>\n</mrow>\n</math>, such that <math alttext=\"upper X\"><mi>X</mi>\n</math>, <math alttext=\"upper Y\"><mi>Y</mi>\n</math>, and <math alttext=\"upper Z\"><mi>Z</mi>\n</math> correspond to <math alttext=\"upper R\"><mi>R</mi>\n</math>, <math alttext=\"upper S\"><mi>S</mi>\n</math>, and <math alttext=\"upper T\"><mi>T</mi>\n</math>, respectively. Since corresponding angles of similar triangles are congruent, it follows that the measure of&nbsp;<math alttext=\"angle upper Z\"><mo>∠</mo><mi>Z</mi></math> is congruent to the measure of <math alttext=\"angle upper T\"><mo>∠</mo><mi>T</mi></math>. It’s given that the measure of <math alttext=\"angle upper Z\"><mo>∠</mo><mi>Z</mi></math> is <math alttext=\"20 degree\"><mn>20</mn><mo>°</mo></math>. Therefore, the measure of <math alttext=\"angle upper T\"><mo>∠</mo><mi>T</mi></math> is&nbsp;<math alttext=\"20 degree\"><mn>20</mn><mo>°</mo></math>.</p>\n<p style=\"text-align: left;\">Choice A is incorrect and may result from a conceptual error.</p>\n<p style=\"text-align: left;\">Choice B is incorrect. This is half the measure of <math alttext=\"angle upper Z\"><mo>∠</mo><mi>Z</mi></math>.</p>\n<p style=\"text-align: left;\">Choice D is incorrect. This is twice the measure of <math alttext=\"angle upper Z\"><mo>∠</mo><mi>Z</mi></math>.</p>","correct_answer":["C"],"has_media":false,"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":[{"label":"A","content_html":"<p><math alttext=\"2 degree\"><mn>2</mn>\n<mo>°</mo></math></p>","ord":0},{"label":"B","content_html":"<p><math alttext=\"10 degree\"><mn>10</mn>\n<mo>°</mo></math></p>","ord":1},{"label":"C","content_html":"<p><math alttext=\"20 degree\"><mn>20</mn>\n<mo>°</mo></math></p>","ord":2},{"label":"D","content_html":"<p><math alttext=\"40 degree\"><mn>40</mn>\n<mo>°</mo></math></p>","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}}