{"id":"cb_question_bank:687964a6-2384-4510-986c-46d8bdd8a9ba","source_id":"cb_question_bank","source_item_id":"687964a6-2384-4510-986c-46d8bdd8a9ba","external_id":"e99677cc-b481-49aa-b1e3-816b48a49b59","ibn":null,"question_id":"c7bed21d","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":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"Quadrilateral upper P prime upper Q prime upper R prime upper S prime is similar to quadrilateral upper P upper Q upper R upper S , where upper P , upper Q , upper R , and upper S correspond to upper P prime , upper Q prime , upper R prime , and upper S prime , respectively. The measure of angle upper P is 30 degree , the measure of angle upper Q is 50 degree , and the measure of angle upper R is 70 degree . The length of each side of upper P prime upper Q prime upper R prime upper S prime is 3 times the length of each corresponding side of upper P upper Q upper R upper S . What is the measure of angle upper P prime ?","stimulus":"","stimulus_html":null,"stem_html":"<p style=\"text-align: left;\">Quadrilateral <math alttext=\"upper P prime upper Q prime upper R prime upper S prime\"><msup><mi>P</mi><mo>'</mo></msup><msup><mi>Q</mi><mo>'</mo></msup><msup><mi>R</mi><mo>'</mo></msup><msup><mi>S</mi><mo>'</mo></msup></math> is similar to quadrilateral <math alttext=\"upper P upper Q upper R upper S\"><mrow>\n\t<mi>P</mi>\n\t<mi>Q</mi>\n\t<mi>R</mi>\n\t<mi>S</mi>\n</mrow>\n</math>, where <math alttext=\"upper P\"><mi>P</mi>\n</math>, <math alttext=\"upper Q\"><mi>Q</mi>\n</math>, <math alttext=\"upper R\"><mi>R</mi>\n</math>, and <math alttext=\"upper S\"><mi>S</mi>\n</math> correspond to <math alttext=\"upper P prime\"><msup><mi>P</mi><mo>'</mo></msup></math>, <math alttext=\"upper Q prime\"><msup><mi>Q</mi><mo>'</mo></msup></math>, <math alttext=\"upper R prime\"><msup><mi>R</mi><mo>'</mo></msup></math>, and <math alttext=\"upper S prime\"><msup><mi>S</mi><mo>'</mo></msup></math>, respectively. The measure of angle <math alttext=\"upper P\"><mi>P</mi>\n</math> is <math alttext=\"30 degree\"><mrow><mn>30</mn></mrow><mo>°</mo></math>, the measure of angle <math alttext=\"upper Q\"><mi>Q</mi>\n</math> is <math alttext=\"50 degree\"><mrow><mn>50</mn></mrow><mo>°</mo></math>, and the measure of angle <math alttext=\"upper R\"><mi>R</mi>\n</math> is <math alttext=\"70 degree\"><mrow><mn>70</mn></mrow><mo>°</mo></math>. The length of each side of <math alttext=\"upper P prime upper Q prime upper R prime upper S prime\"><msup><mi>P</mi><mo>'</mo></msup><msup><mi>Q</mi><mo>'</mo></msup><msup><mi>R</mi><mo>'</mo></msup><msup><mi>S</mi><mo>'</mo></msup></math> is <math alttext=\"3\"><mn>3</mn>\n</math> times the length of each corresponding side of <math alttext=\"upper P upper Q upper R upper S\"><mrow>\n\t<mi>P</mi>\n\t<mi>Q</mi>\n\t<mi>R</mi>\n\t<mi>S</mi>\n</mrow>\n</math>. What is the measure of angle <math alttext=\"upper P prime\"><msup><mi>P</mi><mo>'</mo></msup></math>?</p>","rationale_html":"<p style=\"text-align: left;\">Choice B is correct. It's given that quadrilateral&nbsp;<math alttext=\"upper P prime upper Q prime upper R prime upper S prime\"><msup><mi>P</mi><mo>'</mo></msup><msup><mi>Q</mi><mo>'</mo></msup><msup><mi>R</mi><mo>'</mo></msup><msup><mi>S</mi><mo>'</mo></msup></math> is similar to quadrilateral <math alttext=\"upper P upper Q upper R upper S\"><mi>P</mi><mi>Q</mi><mi>R</mi><mi>S</mi></math>, where <math alttext=\"upper P\"><mi>P</mi>\n</math>, <math alttext=\"upper Q\"><mi>Q</mi>\n</math>, <math alttext=\"upper R\"><mi>R</mi>\n</math>, and <math alttext=\"upper S\"><mi>S</mi>\n</math> correspond to <math alttext=\"upper P prime\"><msup><mi>P</mi><mo>'</mo></msup></math>, <math alttext=\"upper Q prime\"><msup><mi>Q</mi><mo>'</mo></msup></math>, <math alttext=\"upper R prime\"><msup><mi>R</mi><mo>'</mo></msup></math>, and <math alttext=\"upper S prime\"><msup><mi>S</mi><mo>'</mo></msup></math>, respectively. Since corresponding angles of similar quadrilaterals are congruent, it follows that the measure of angle <math alttext=\"upper P\"><mi>P</mi>\n</math> is equal to the measure of angle <math alttext=\"upper P prime\"><msup><mi>P</mi><mo>'</mo></msup></math>. It's given that the measure of angle <math alttext=\"upper P\"><mi>P</mi>\n</math> is <math alttext=\"30 degree\"><mn>30</mn><mo>°</mo></math>. Therefore, the measure of angle&nbsp;<math alttext=\"upper P prime\"><msup><mi>P</mi><mo>'</mo></msup></math> is <math alttext=\"30 degree\"><mn>30</mn><mo>°</mo></math>.</p>\n<p style=\"text-align: left;\">Choice A is incorrect. This is&nbsp;<math alttext=\"one third\"><mfrac><mn>1</mn><mn>3</mn></mfrac></math> the measure of angle <math alttext=\"upper P prime\"><msup><mi>P</mi><mo>'</mo></msup></math>.</p>\n<p style=\"text-align: left;\">Choice C is incorrect and may result from conceptual or calculation errors.</p>\n<p style=\"text-align: left;\">Choice D is incorrect. This is <math alttext=\"3\"><mn>3</mn>\n</math> times the measure of angle <math alttext=\"upper P prime\"><msup><mi>P</mi><mo>'</mo></msup></math>.</p>","correct_answer":["B"],"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=\"10 degree\"><mrow><mn>10</mn></mrow><mo>°</mo></math></p>","ord":0},{"label":"B","content_html":"<p><math alttext=\"30 degree\"><mrow><mn>30</mn></mrow><mo>°</mo></math></p>","ord":1},{"label":"C","content_html":"<p><math alttext=\"40 degree\"><mrow><mn>40</mn></mrow><mo>°</mo></math></p>","ord":2},{"label":"D","content_html":"<p><math alttext=\"90 degree\"><mrow><mn>90</mn></mrow><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}}