{"id":"cb_question_bank:a81b6c36-0ac1-43de-89f3-4aa74c354238","source_id":"cb_question_bank","source_item_id":"a81b6c36-0ac1-43de-89f3-4aa74c354238","external_id":"4d53ed15-713b-4aa2-8943-17060404b617","ibn":null,"question_id":"0bb39de4","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":"Triangles upper A upper B upper C and upper D upper E upper F are congruent, where upper A corresponds to upper D , and upper B and upper E are right angles. The measure of angle upper A is 18 degree . What is the measure of angle upper F ?","stimulus":"","stimulus_html":null,"stem_html":"<p style=\"text-align: left;\">Triangles <math alttext=\"upper A upper B upper C\"><mrow>\n\t<mi>A</mi>\n\t<mi>B</mi>\n\t<mi>C</mi>\n</mrow>\n</math> and <math alttext=\"upper D upper E upper F\"><mrow>\n\t<mi>D</mi>\n\t<mi>E</mi>\n\t<mi>F</mi>\n</mrow>\n</math> are congruent, where <math alttext=\"upper A\"><mi>A</mi>\n</math> corresponds to <math alttext=\"upper D\"><mi>D</mi>\n</math>, and <math alttext=\"upper B\"><mi>B</mi>\n</math> and <math alttext=\"upper E\"><mi>E</mi>\n</math> are right angles. The measure of angle <math alttext=\"upper A\"><mi>A</mi>\n</math> is <math alttext=\"18 degree\"><mrow><mn>18</mn></mrow><mo>°</mo></math>. What is the measure of angle <math alttext=\"upper F\"><mi>F</mi>\n</math>?</p>","rationale_html":"<p>Choice B is correct. It’s given that triangle <math alttext=\"upper A upper B upper C\"><mrow>\n\t<mi>A</mi>\n\t<mi>B</mi>\n\t<mi>C</mi>\n</mrow>\n</math> is congruent to triangle <math alttext=\"upper D upper E upper F\"><mrow>\n\t<mi>D</mi>\n\t<mi>E</mi>\n\t<mi>F</mi>\n</mrow>\n</math>. Corresponding angles of congruent triangles are congruent and, therefore, have equal measure. It’s given that angle <math alttext=\"upper A\"><mi>A</mi>\n</math> corresponds to angle <math alttext=\"upper D\"><mi>D</mi>\n</math>, and that the measure of angle <math alttext=\"upper A\"><mi>A</mi>\n</math> is <math alttext=\"18 degree\"><mn>18</mn><mo>°</mo></math>. It's also given that the measures of angles <math alttext=\"upper B\"><mi>B</mi>\n</math> and <math alttext=\"upper E\"><mi>E</mi>\n</math> are <math alttext=\"90 degree\"><mn>90</mn><mo>°</mo></math>. Since these angles have equal measure, they are corresponding angles. It follows that angle <math alttext=\"upper C\"><mi>C</mi>\n</math> corresponds to angle <math alttext=\"upper F\"><mi>F</mi>\n</math>. Let <math alttext=\"x degree\"><mi>x</mi><mo>°</mo></math> represent the measure of angle <math alttext=\"upper C\"><mi>C</mi>\n</math>. Since the sum of the measures of the interior angles of a triangle is <math alttext=\"180 degree\"><mn>180</mn><mo>°</mo></math>, it follows that <math alttext=\"18 degree plus 90 degree plus x degree  equals 180 degree\"><mn>18</mn><mo>°</mo><mo>+</mo><mn>90</mn><mo>°</mo><mo>+</mo><mi>x</mi><mo>°</mo><mo>=</mo><mn>180</mn><mo>°</mo></math>, or <math alttext=\"108 degree plus x degree  equals 180 degree\"><mn>108</mn><mo>°</mo><mo>+</mo><mi>x</mi><mo>°</mo><mo>=</mo><mn>180</mn><mo>°</mo></math>. Subtracting <math alttext=\"108 degree\"><mn>108</mn><mo>°</mo></math> from both sides of this equation yields <math alttext=\"x degree  equals 72 degree\"><mi>x</mi><mo>°</mo><mo>=</mo><mn>72</mn><mo>°</mo></math>. Therefore, the measure of angle <math alttext=\"upper C\"><mi>C</mi>\n</math> is <math alttext=\"72 degree\"><mn>72</mn><mo>°</mo></math>. Since angle <math alttext=\"upper C\"><mi>C</mi>\n</math> corresponds to angle <math alttext=\"upper F\"><mi>F</mi>\n</math>, it follows that the measure of angle <math alttext=\"upper F\"><mi>F</mi>\n</math> is also <math alttext=\"72 degree\"><mn>72</mn><mo>°</mo></math>.</p>\n<p>Choice A is incorrect. This is the measure of angle <math alttext=\"upper D\"><mi>D</mi>\n</math>, not the measure of angle <math alttext=\"upper F\"><mi>F</mi>\n</math>.</p>\n<p>Choice C is incorrect. This is the measure of angle <math alttext=\"upper E\"><mi>E</mi>\n</math>, not the measure of angle <math alttext=\"upper F\"><mi>F</mi>\n</math>.</p>\n<p>Choice D is incorrect. This is the sum of the measures of angles <math alttext=\"upper E\"><mi>E</mi>\n</math> and <math alttext=\"upper F\"><mi>F</mi>\n</math>, not the measure of angle <math alttext=\"upper F\"><mi>F</mi>\n</math>.</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=\"18 degree\"><mn>18</mn>\n<mo>°</mo></math></p>","ord":0},{"label":"B","content_html":"<p><math alttext=\"72 degree\"><mn>72</mn>\n<mo>°</mo></math></p>","ord":1},{"label":"C","content_html":"<p><math alttext=\"90 degree\"><mn>90</mn>\n<mo>°</mo></math></p>","ord":2},{"label":"D","content_html":"<p><math alttext=\"162 degree\"><mn>162</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}}