{"id":"cb_question_bank:9605d736-8cf7-47fe-9cbb-7a5151e79bb8","source_id":"cb_question_bank","source_item_id":"9605d736-8cf7-47fe-9cbb-7a5151e79bb8","external_id":"0f1a7b12-733e-45ba-a7fc-021a951885f5","ibn":null,"question_id":"f1c1e971","program":"SAT","module":"math","domain_code":"S","domain":"Geometry and Trigonometry","skill_code":"S.D.","skill":"Circles","difficulty":"M","score_band":5,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"The measure of angle upper R is StartFraction 2 pi Over 3 EndFraction radians. The measure of angle upper T is StartFraction 5 pi Over 12 EndFraction radians greater than the measure of angle upper R . What is the measure of angle upper T , in degrees ?","stimulus":"","stimulus_html":null,"stem_html":"

The measure of angle R\n is \n\t\n\t\t\n\t\t\t2\n\t\t\tπ\n\t\t\n\t\t3\n\t\n\n radians. The measure of angle T\n is \n\t\n\t\t\n\t\t\t5\n\t\t\tπ\n\t\t\n\t\t12\n\t\n\n radians greater than the measure of angle R\n. What is the measure of angle T\n, in degrees?

","rationale_html":"

Choice C is correct. It’s given that the measure of angle R\n is 2π3 radians, and the measure of angle T\n is 5π12 radians greater than the measure of angle R\n. Therefore, the measure of angle T\n is equal to 2π3+5π12 radians. Multiplying 2π3 by 44 to get a common denominator with 5π12 yields 8π12. Therefore, 2π3+5π12 is equivalent to 8π12+5π12, or 13π12. Therefore, the measure of angle T\n is 13π12 radians. The measure of angle T\n, in degrees, can be found by multiplying its measure, in radians, by 180π. This yields 13π12×180π, which is equivalent to 195\n degrees. Therefore, the measure of angle T\n is 195\n degrees.

\n

Choice A is incorrect. This is the number of degrees that the measure of angle T\n is greater than the measure of angle R\n.

\n

Choice B is incorrect. This is the measure of angle R\n, in degrees.

\n

Choice D is incorrect and may result from conceptual or calculation errors.

","correct_answer":["C"],"has_media":false,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.841000+00:00","source_updated_at":"2023-08-02T20:25:59.841000+00:00","options":[{"label":"A","content_html":"

75\n

","ord":0},{"label":"B","content_html":"

120\n

","ord":1},{"label":"C","content_html":"

195\n

","ord":2},{"label":"D","content_html":"

390\n

","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}}