{"id":"cb_question_bank:0485784b-588b-4744-8b26-a0d5b3a792ae","source_id":"cb_question_bank","source_item_id":"0485784b-588b-4744-8b26-a0d5b3a792ae","external_id":"8a0d3a20-6326-4fe6-a269-38ef70418956","ibn":null,"question_id":"e10d8313","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":"From left to right, horizontal line segment upper P upper V includes the following points: Upper P Upper Q Upper R Upper S Upper T Upper V Points upper X and upper U are each below line segment upper P upper V. From left to right, the following 2 overlapping triangles are formed between points on line segment upper P upper V and points upper X and upper U: Triangle upper Q upper X upper S Triangle upper R upper U upper T Line segments upper R upper U and upper S upper X intersect at point upper W. A note indicates the figure is not drawn to scale. In the figure shown, points upper Q , upper R , upper S , and upper T lie on line segment upper P upper V , and line segment upper R upper U intersects line segment upper S upper X at point upper W . The measure of angle upper S upper Q upper X is 48 degree , the measure of angle upper S upper X upper Q is 86 degree , the measure of angle upper S upper W upper U is 85 degree , and the measure of angle upper V upper T upper U is 162 degree . What is the measure, in degrees, of angle upper T upper U upper R ?","stimulus":"","stimulus_html":null,"stem_html":"

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In the figure shown, points Q\n, R\n, S\n, and T\n lie on line segment \n\tP\n\tV\n\n, and line segment \n\tR\n\tU\n\n intersects line segment \n\tS\n\tX\n\n at point W\n. The measure of ∠SQX is 48°, the measure of ∠SXQ is 86°, the measure of ∠SWU is 85°, and the measure of ∠VTU is 162°. What is the measure, in degrees, of ∠TUR? 

","rationale_html":"

The correct answer is 123\n. The triangle angle sum theorem states that the sum of the measures of the interior angles of a triangle is 180\n degrees. It's given that the measure of ∠SQX is 48° and the measure of ∠SXQ is 86°. Since points S\n, Q\n, and X\n form a triangle, it follows from the triangle angle sum theorem that the measure, in degrees, of ∠QSX is 180-48-86, or 46\n. It's also given that the measure of ∠SWU is 85°. Since ∠SWU and ∠SWR are supplementary angles, the sum of their measures is 180\n degrees. It follows that the measure, in degrees, of ∠SWR is 180-85, or 95\n. Since points R\n, S\n, and W\n form a triangle, and ∠RSW is the same angle as ∠QSX, it follows from the triangle angle sum theorem that the measure, in degrees, of ∠WRS is 180-46-95, or 39\n. It's given that the measure of ∠VTU is 162°. Since ∠VTU and ∠STU are supplementary angles, the sum of their measures is 180\n degrees. It follows that the measure, in degrees, of ∠STU is 180-162, or 18. Since points R\n, T\n, and U\n form a triangle, and ∠URT is the same angle as ∠WRS, it follows from the triangle angle sum theorem that the measure, in degrees, of ∠TUR is 180-39-18, or 123.

","correct_answer":["123"],"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}}