{"id":"cb_question_bank:2329cf42-ea2f-4a2f-a69d-609b310dd7ca","source_id":"cb_question_bank","source_item_id":"2329cf42-ea2f-4a2f-a69d-609b310dd7ca","external_id":"baefd1d0-91cf-4b82-9c41-2145510636af","ibn":null,"question_id":"cbe8ca31","program":"SAT","module":"math","domain_code":"S","domain":"Geometry and Trigonometry","skill_code":"S.B.","skill":"Lines, angles, and triangles","difficulty":"E","score_band":2,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"In triangle upper X upper Y upper Z , the measure of angle upper X is 24 degree and the measure of angle upper Y is 98 degree . What is the measure of angle upper Z ?","stimulus":"","stimulus_html":null,"stem_html":"<p>In <math alttext=\"triangle upper X upper Y upper Z\"><mo>△</mo><mi>X</mi><mi>Y</mi><mi>Z</mi></math>, the measure of <math alttext=\"angle upper X\"><mo>∠</mo><mi>X</mi></math><em> </em>is <math alttext=\"24 degree\"><mn>24</mn>\n<mo>°</mo></math> and the measure of <math alttext=\"angle upper Y\"><mo>∠</mo><mi>Y</mi></math><em> </em>is <math alttext=\"98 degree\"><mn>98</mn>\n<mo>°</mo></math>. What is the measure of <math alttext=\"angle upper Z\"><mo>∠</mo><mi>Z</mi></math>?</p>","rationale_html":"<p style=\"text-align: left;\">Choice A is correct. The triangle angle sum theorem states that the sum of the measures of the interior angles of a triangle is <math alttext=\"180 degree\"><mn>180</mn><mo>°</mo></math>. It's given that in&nbsp;<math alttext=\"triangle upper X upper Y upper Z\"><mo>△</mo><mi>X</mi><mi>Y</mi><mi>Z</mi></math>, the measure of&nbsp;<math alttext=\"angle upper X\"><mo>∠</mo><mi>X</mi></math> is&nbsp;<math alttext=\"24 degree\"><mn>24</mn><mo>°</mo></math> and the measure of&nbsp;<math alttext=\"angle upper Y\"><mo>∠</mo><mi>Y</mi></math> is&nbsp;<math alttext=\"98 degree\"><mn>98</mn><mo>°</mo></math>. It follows that the measure of&nbsp;<math alttext=\"angle upper Z\"><mo>∠</mo><mi>Z</mi></math> is&nbsp;<math alttext=\"left parenthesis 180 minus 24 minus 98 right parenthesis degree\"><mfenced><mrow><mn>180</mn><mo>-</mo><mn>24</mn><mo>-</mo><mn>98</mn></mrow></mfenced><mo>°</mo></math>, or&nbsp;<math alttext=\"58 degree\"><mn>58</mn><mo>°</mo></math>.</p>\n<p style=\"text-align: left;\">Choice B is incorrect and may result from conceptual or calculation errors.</p>\n<p style=\"text-align: left;\">Choice C is incorrect. This is the sum of the measures of <math alttext=\"angle upper X\"><mo>∠</mo><mi>X</mi></math> and&nbsp;<math alttext=\"angle upper Y\"><mo>∠</mo><mi>Y</mi></math>, not the measure of&nbsp;<math alttext=\"angle upper Z\"><mo>∠</mo><mi>Z</mi></math>.</p>\n<p style=\"text-align: left;\">Choice D is incorrect and may result from conceptual or calculation errors.</p>","correct_answer":["A"],"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=\"58 degree\"><mn>58</mn>\n<mo>°</mo></math></p>","ord":0},{"label":"B","content_html":"<p><math alttext=\"74 degree\"><mn>74</mn>\n<mo>°</mo></math></p>","ord":1},{"label":"C","content_html":"<p><math alttext=\"122 degree\"><mn>122</mn>\n<mo>°</mo></math></p>","ord":2},{"label":"D","content_html":"<p><math alttext=\"212 degree\"><mn>212</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}}