{"id":"cb_question_bank:b8e65f4f-03bc-4883-8a68-666a3f65d9cd","source_id":"cb_question_bank","source_item_id":"b8e65f4f-03bc-4883-8a68-666a3f65d9cd","external_id":null,"ibn":"025648-DC","question_id":"95ba2d09","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":"In the xy -plane above, points P , Q , R , and T lie on the circle with center O . The degree measures of angles P O Q and R O T are each 30°. What is the radian measure of angle Q O R ?","stimulus":"The figure presents a circle in the x y plane, with the origin labeled O. The center of the circle lies at the origin. There are 4 points, T, R, Q, and P, labeled clockwise on the circle. Point T lies on the x axis, directly to the left of the origin, and has coordinates negative 1 comma 0. Point R lies above the x axis, and to the left of the y axis. Point Q lies above the x axis and to the right of the y axis. Point P lies on the x axis, directly to the right of the origin, and has coordinates 1 comma 0. Points R and Q appear to be symmetric with respect to the y axis. Four line segments are drawn from the origin to each of the four points on the circle.","stimulus_html":"
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\"The
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\n","stem_html":"

In the xy-plane above, points P, Q, R, and T lie on the circle with center O. The degree measures of angles \"P and \"R are each 30°. What is the radian measure of angle \"Q ?

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Choice C is correct. Because points T, O, and P all lie on the x-axis, they form a line. Since the angles on a line add up to \"180, and it’s given that angles POQ and ROT each measure \"30, it follows that the measure of angle QOR is \"180. Since the arc of a complete circle is \"360 or \"2 radians, a proportion can be set up to convert the measure of angle QOR from degrees to radians: \"the, where x is the radian measure of angle QOR. Multiplying each side of the proportion by \"2 gives \"360. Solving for x gives \"the, or \"two.

Choice A is incorrect and may result from subtracting only angle POQ from \"180to get a value of \"150and then finding the radian measure equivalent to that value. Choice B is incorrect and may result from a calculation error. Choice D is incorrect and may result from calculating the sum of the angle measures, in radians, of angles POQ and ROT.

 

\n","correct_answer":["C"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.619000+00:00","source_updated_at":"2023-08-02T20:25:59.619000+00:00","options":[{"label":"A","content_html":"

\"five

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

\"three

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

\"two

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

\"one

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