{"id":"cb_question_bank:dc2406de-15b4-4152-9a3f-c10992d5a6bc","source_id":"cb_question_bank","source_item_id":"dc2406de-15b4-4152-9a3f-c10992d5a6bc","external_id":"64da6245-4314-4da9-817e-46dcdd9dc29d","ibn":null,"question_id":"4ff7b652","program":"SAT","module":"math","domain_code":"S","domain":"Geometry and Trigonometry","skill_code":"S.B.","skill":"Lines, angles, and triangles","difficulty":"M","score_band":4,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"Right triangles upper L upper M upper N and upper P upper Q upper R are similar, where upper L and upper M correspond to upper P and upper Q , respectively. Angle upper M has a measure of 53 degree . What is the measure of angle upper Q ?","stimulus":"","stimulus_html":null,"stem_html":"<p style=\"text-align: left;\">Right triangles <math alttext=\"upper L upper M upper N\"><mrow>\n\t<mi>L</mi>\n\t<mi>M</mi>\n\t<mi>N</mi>\n</mrow>\n</math> and <math alttext=\"upper P upper Q upper R\"><mrow>\n\t<mi>P</mi>\n\t<mi>Q</mi>\n\t<mi>R</mi>\n</mrow>\n</math> are similar, where <math alttext=\"upper L\"><mi>L</mi>\n</math> and <math alttext=\"upper M\"><mi>M</mi>\n</math> correspond to <math alttext=\"upper P\"><mi>P</mi>\n</math> and <math alttext=\"upper Q\"><mi>Q</mi>\n</math>, respectively. Angle <math alttext=\"upper M\"><mi>M</mi>\n</math> has a measure of <math alttext=\"53 degree\"><mn>53</mn>\n<mo>°</mo></math>. What is the measure of angle <math alttext=\"upper Q\"><mi>Q</mi>\n</math>?</p>","rationale_html":"<p>Choice B is correct. It’s given that triangle <math alttext=\"upper L upper M upper N\"><mrow>\n\t<mi>L</mi>\n\t<mi>M</mi>\n\t<mi>N</mi>\n</mrow>\n</math> is similar to triangle <math alttext=\"upper P upper Q upper R\"><mrow>\n\t<mi>P</mi>\n\t<mi>Q</mi>\n\t<mi>R</mi>\n</mrow>\n</math>. Corresponding angles of similar triangles are congruent. Since angle <math alttext=\"upper M\"><mi>M</mi>\n</math> and angle <math alttext=\"upper Q\"><mi>Q</mi>\n</math> correspond to each other, they must be congruent. Therefore, if the measure of angle <math alttext=\"upper M\"><mi>M</mi>\n</math> is <math alttext=\"53 degree\"><mn>53</mn><mo>°</mo></math>, then the measure of angle <math alttext=\"upper Q\"><mi>Q</mi>\n</math> is also&nbsp;<math alttext=\"53 degree\"><mn>53</mn><mo>°</mo></math>.</p>\n<p>Choice A is incorrect and may result from concluding that angle <math alttext=\"upper M\"><mi>M</mi>\n</math> and angle <math alttext=\"upper Q\"><mi>Q</mi>\n</math> are complementary rather than congruent.</p>\n<p>Choice C is incorrect and may result from concluding that angle <math alttext=\"upper M\"><mi>M</mi>\n</math> and angle <math alttext=\"upper Q\"><mi>Q</mi>\n</math> are supplementary rather than congruent.</p>\n<p>Choice D is incorrect and may result from conceptual or calculation errors.</p>","correct_answer":["B"],"has_media":false,"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":"<p><math alttext=\"37 degree\"><mn>37</mn>\n<mo>°</mo></math></p>","ord":0},{"label":"B","content_html":"<p><math alttext=\"53 degree\"><mn>53</mn>\n<mo>°</mo></math></p>","ord":1},{"label":"C","content_html":"<p><math alttext=\"127 degree\"><mn>127</mn>\n<mo>°</mo></math></p>","ord":2},{"label":"D","content_html":"<p><math alttext=\"143 degree\"><mn>143</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}}