{"id":"cb_question_bank:53f8ecd1-73ee-47a9-bc24-87ff42030076","source_id":"cb_question_bank","source_item_id":"53f8ecd1-73ee-47a9-bc24-87ff42030076","external_id":"84bcf173-28fe-47bf-bf15-075592753ee0","ibn":null,"question_id":"249d3f80","program":"SAT","module":"math","domain_code":"S","domain":"Geometry and Trigonometry","skill_code":"S.D.","skill":"Circles","difficulty":"H","score_band":6,"answer_type":"spr","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"Point upper O is the center of a circle. The measure of arc upper R upper S on this circle is 100 degree . What is the measure, in degrees, of its associated angle upper R upper O upper S ?","stimulus":"","stimulus_html":null,"stem_html":"<p style=\"text-align: left;\">Point <math alttext=\"upper O\"><mi>O</mi>\n</math> is the center of a circle. The measure of arc <math alttext=\"upper R upper S\"><mrow>\n\t<mi>R</mi>\n\t<mi>S</mi>\n</mrow>\n</math> on this circle is <math alttext=\"100 degree\"><mrow><mn>100</mn></mrow><mo>°</mo></math>. What is the measure, in degrees, of its associated angle <math alttext=\"upper R upper O upper S\"><mi>R</mi><mi>O</mi><mi>S</mi></math>?</p>","rationale_html":"<p style=\"text-align: left;\">The correct answer is <math alttext=\"100\"><mn>100</mn>\n</math>. It's given that point <math alttext=\"upper O\"><mi>O</mi>\n</math> is the center of a circle and the measure of arc <math alttext=\"upper R upper S\"><mi>R</mi><mi>S</mi></math> on the circle is&nbsp;<math alttext=\"100 degree\"><mn>100</mn><mo>°</mo></math>. It follows that points <math alttext=\"upper R\"><mi>R</mi>\n</math> and <math alttext=\"upper S\"><mi>S</mi>\n</math> lie on the circle. Therefore,&nbsp;<math alttext=\"ModifyingAbove upper O upper R With bar\"><mover><mrow><mi>O</mi><mi>R</mi></mrow><mo>¯</mo></mover></math> and&nbsp;<math alttext=\"ModifyingAbove upper O upper S With bar\"><mover><mrow><mi>O</mi><mi>S</mi></mrow><mo>¯</mo></mover></math> are radii of the circle. A central angle is an angle formed by two radii of a circle, with its vertex at the center of the circle. Therefore, <math alttext=\"angle upper R upper O upper S\"><mo>∠</mo><mi>R</mi><mi>O</mi><mi>S</mi></math> is a central angle. Because the degree measure of an arc is equal to the measure of its associated central angle, it follows that the measure, in degrees, of <math alttext=\"angle upper R upper O upper S\"><mo>∠</mo><mi>R</mi><mi>O</mi><mi>S</mi></math> is <math alttext=\"100\"><mn>100</mn>\n</math>.</p>","correct_answer":["100"],"has_media":false,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.840000+00:00","source_updated_at":"2023-08-02T20:25:59.840000+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}}