{"id":"cb_question_bank:111b9e49-eab3-456b-8179-7e6b6929106e","source_id":"cb_question_bank","source_item_id":"111b9e49-eab3-456b-8179-7e6b6929106e","external_id":null,"ibn":"026874-DC","question_id":"c8d60e48","program":"SAT","module":"math","domain_code":"S","domain":"Geometry and Trigonometry","skill_code":"S.B.","skill":"Lines, angles, and triangles","difficulty":"E","score_band":3,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"In the given triangle, the length of side A, B equals the length of side A, C and angle A, B C has a measure of 67 degrees . What is the value of x ?","stimulus":"The figure presents triangle B A, C, such that side B C is horizontal and vertex A, is above side B C. Angle A, is labeled x degrees.","stimulus_html":"<div class=\"stimulus_reference \">\n        <div class=\"standalone_image \">\n          <img src=\"/api/assets/d8d815555ea560970fd7b8b84c4531442ebfc4298dd73ed2f35f9d3615124b7c\" alt=\"The figure presents triangle B A, C, such that side B C is horizontal and vertex A, is above side B C. Angle A, is labeled x degrees.\" width=\"89\" height=\"101\"></div>\n      </div>\n","stem_html":"<p class=\"stem_paragraph \">In the given triangle, <span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/a99b471a5ed6678f393e1bf9f1ed72748aee39c1bc308005a34ff4aa9eeac8af\" alt=\"the length of side A, B equals the length of side A, C \"></span></span> and <span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/633aa31a45153ca95c4ffa97dad6e534f3b02175e7c8509bf3b96de27ab427fd\" alt=\"angle A, B C \"></span></span> has a measure of <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/3c7b0cc398a70ae6d69b295dd03d128f216dbd6f9e9e8b119e471bfa4c326bb6\" alt=\"67 degrees\"></span>. What is the value of <span class=\"italic\">x</span> ?</p>\n","rationale_html":"<p>Choice B is correct. Since <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/a99b471a5ed6678f393e1bf9f1ed72748aee39c1bc308005a34ff4aa9eeac8af\" alt=\"the length of A, B equals the length of A, C\"></span>, the measures of their corresponding angles, <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/633aa31a45153ca95c4ffa97dad6e534f3b02175e7c8509bf3b96de27ab427fd\" alt=\"angle A, B C \"></span> and <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/c13636b4422b1a09e8b0d4b6a41224057d78835f4f064371e851a101024d4f5e\" alt=\"angle A, C B\"></span>, are equal. Since <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/633aa31a45153ca95c4ffa97dad6e534f3b02175e7c8509bf3b96de27ab427fd\" alt=\"angle A, B C \"></span> has a measure of <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/3c7b0cc398a70ae6d69b295dd03d128f216dbd6f9e9e8b119e471bfa4c326bb6\" alt=\"67 degrees\"></span>, the measure of <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/c13636b4422b1a09e8b0d4b6a41224057d78835f4f064371e851a101024d4f5e\" alt=\"angle A, C B\"></span> is also <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/3c7b0cc398a70ae6d69b295dd03d128f216dbd6f9e9e8b119e471bfa4c326bb6\" alt=\"67 degrees\"></span>. Since the sum of the measures of the interior angles in a triangle is <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/ec0041af7817f5d2c927cbdf134a73bc148941d5c3e5ddb80665e5fac696f97e\" alt=\"180 degrees\"></span>, it follows that <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/dbdc318a76db09fbd8ad70ea30595f60a3704bb3237e3b76e574a5e2639f014c\" alt=\"67 plus 67, plus x, equals 180\"></span>, or <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/262cccf6c8b102b8af810b7f8740891b8cb1195312293a56163af4848452e779\" alt=\"134 plus x, equals 180\"></span>. Subtracting by 134 on both sides of this equation yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/e7ee4504565e68784392f0bf2373eee7c4749425fa9a3c256d13d97d62484983\" alt=\"x equals 46\"></span>.</p><p>Choices A, C, and D are incorrect and may result from calculation errors.</p><p></p>\n","correct_answer":["B"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.621000+00:00","source_updated_at":"2023-08-02T20:25:59.621000+00:00","options":[{"label":"A","content_html":"<p class=\"choice_paragraph \">36</p>\n","ord":0},{"label":"B","content_html":"<p class=\"choice_paragraph \">46</p>\n","ord":1},{"label":"C","content_html":"<p class=\"choice_paragraph \">58</p>\n","ord":2},{"label":"D","content_html":"<p class=\"choice_paragraph \">70</p>\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}}