{"id":"cb_question_bank:0053ca91-ad76-40ab-8f72-b5b3ced85bee","source_id":"cb_question_bank","source_item_id":"0053ca91-ad76-40ab-8f72-b5b3ced85bee","external_id":"dbda3b6a-f820-4919-8708-c6088f04c080","ibn":null,"question_id":"6d99b141","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":"spr","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"Triangle upper A upper C upper D partially overlaps triangle upper E upper B upper D. Point upper C is on line segment upper B upper D. Point upper E is on line segment upper A upper D. The measure of angle upper A upper E upper B is x°. A note indicates the figure is not drawn to scale. In the figure, upper A upper C equals upper C upper D . The measure of angle upper E upper B upper C is 45 degree , and the measure of angle upper A upper C upper D is 104 degree . What is the value of x ?","stimulus":"","stimulus_html":null,"stem_html":"

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In the figure, \n\t\n\t\tA\n\t\tC\n\t\n\t=\n\t\n\t\tC\n\t\tD\n\t\n\n. The measure of angle EBC is 45°, and the measure of angle ACD is 104°. What is the value of x\n?

","rationale_html":"

The correct answer is 83\n. It's given that in the figure, \n\t\n\t\tA\n\t\tC\n\t\n\t=\n\t\n\t\tC\n\t\tD\n\t\n\n. Thus, triangle \n\tA\n\tC\n\tD\n\n is an isosceles triangle and the measure of angle CDA is equal to the measure of angle CAD. The sum of the measures of the interior angles of a triangle is 180°. Thus, the sum of the measures of the interior angles of triangle \n\tA\n\tC\n\tD\n\n is 180°. It's given that the measure of angle \n\tA\n\tC\n\tD\n\n is 104°. It follows that the sum of the measures of angles CDA and CAD is 180-104°, or 76°. Since the measure of angle CDA is equal to the measure of angle CAD, the measure of angle CDA is half of 76°, or 38°. The sum of the measures of the interior angles of triangle \n\tB\n\tD\n\tE\n\n is 180°. It's given that the measure of angle EBC is 45°. Since the measure of angle BDE, which is the same angle as angle CDA, is 38°, it follows that the measure of angle DEB is 180-45-38°, or 97°. Since angle DEB and angle AEB form a straight line, the sum of the measures of these angles is 180°. It's given in the figure that the measure of angle AEB is x°. It follows that 97+x=180. Subtracting 97\n from both sides of this equation yields \n\tx\n\t=\n\t83\n\n.

","correct_answer":["83"],"has_media":true,"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":[],"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}}