{"id":"cb_question_bank:9db9f6af-3b1a-4ef9-a97c-c5bc43729a60","source_id":"cb_question_bank","source_item_id":"9db9f6af-3b1a-4ef9-a97c-c5bc43729a60","external_id":null,"ibn":"027075-DC","question_id":"5733ce30","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 figure, side A C extends to point D . If the measure of angle B A C is equal to the measure of angle B C A , what is the value of x ?","stimulus":"The figure presents triangle A B C, where side A C is horizontal, vertex A is to the left of vertex C, vertex B is above side A C, and the measure of angle A B C is labeled x degrees. Side A C extends horizontally to the right to point D, and the angle, B C D, that is above line segment C D and to the right of side B C has a measure of one hundred ten degrees.","stimulus_html":"<div class=\"stimulus_reference \">\n        <div class=\"standalone_image \">\n          <img src=\"/api/assets/a086f0b58cc12de0981d3cc03092d55501bbae7a4661201c97b3cb1a7374bf16\" alt=\"The figure presents triangle A B C, where side A C is horizontal, vertex A is to the left of vertex C, vertex B is above side A C, and the measure of angle A B C is labeled x degrees. Side A C extends horizontally to the right to point D, and the angle, B C D, that is above line segment C D and to the right of side B C has a measure of one hundred ten degrees. \" width=\"139\" height=\"115\"></div>\n      </div>\n","stem_html":"<p class=\"stem_paragraph \">In the given figure, <span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/838c37eb26f8e7bea94de28d37cede03fda6bc1cb7121288f537103ca3516078\" alt=\"side A C \"></span></span> extends to point <span class=\"italic\">D</span>. If the measure of <span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/bda7ab78500c35aa5c437751b3ed8239ff96d2e42967128997a709a838fa5d37\" alt=\"angle B A C \"></span></span> is equal to the measure of <span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/b2c118f50ea75a5e355b6a9e0fa00e9b390d6b7b99e2546eac734e6f336eb5fa\" alt=\"angle B C A\"></span></span>, what is the value of <span class=\"italic\">x</span> ?</p>\n","rationale_html":"<p>Choice D is correct. Since <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/f4b422887f2b706508b49515b52358d80702c3d27f1b2786053443bef1278c8b\" alt=\"angle B C D \"></span> and <span class=\"italic\"></span><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/b2c118f50ea75a5e355b6a9e0fa00e9b390d6b7b99e2546eac734e6f336eb5fa\" alt=\"angle B C A\"></span> form a linear pair of angles, their measures sum to 180°. It’s given that the measure of <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/f4b422887f2b706508b49515b52358d80702c3d27f1b2786053443bef1278c8b\" alt=\"angle B C D\"></span> is 110°. Therefore, <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/b004e8bc837f080a1e91c25da1782323c73eb92640e5293dcb29f31647d1e12b\" alt=\"110 degrees plus angle B C A, equals 180 degrees\"></span>. Subtracting 110° from both sides of this equation gives the measure of <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/b2c118f50ea75a5e355b6a9e0fa00e9b390d6b7b99e2546eac734e6f336eb5fa\" alt=\"angle B C A\"></span> as 70°. It’s also given that the measure of <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/bda7ab78500c35aa5c437751b3ed8239ff96d2e42967128997a709a838fa5d37\" alt=\"angle B A C\"></span> is equal to the measure of <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/b2c118f50ea75a5e355b6a9e0fa00e9b390d6b7b99e2546eac734e6f336eb5fa\" alt=\"angle B C A\"></span>. Thus, the measure of <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/bda7ab78500c35aa5c437751b3ed8239ff96d2e42967128997a709a838fa5d37\" alt=\"angle B A C\"></span> is also 70°. The measures of the interior angles of a triangle sum to 180°. Thus, <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/78e06792fc4d48bc14aa3bba326bed21940312bb9c7acf0273e6c24c00baffc4\" alt=\"70 degrees, plus 70 degrees, plus x degrees, equals 180 degrees\"></span>. Combining like terms on the left-hand side of this equation yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/ff540fb295695ac6f9b1345830ef3d1feea1847d1e7e1b19c226e66934e8a9db\" alt=\"140 degrees plus x degrees, equals 180 degrees\"></span>. Subtracting 140° from both sides of this equation yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/7cb13086750252946c77a7851937f585e7b9ac36b342b6411e41e658e2da91db\" alt=\"x degrees equals 40 degrees\"></span>, or <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/ef256d38b97bb7060f7cc9fa2f435cbf46285888e22a7234e27ff74e53121b07\" alt=\"x equals 40\"></span>.</p><p>Choice A is incorrect. This is the value of the measure of <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/f4b422887f2b706508b49515b52358d80702c3d27f1b2786053443bef1278c8b\" alt=\"angle B C D\"></span>. Choice B is incorrect. This is the value of the measure of each of the other two interior angles, <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/b2c118f50ea75a5e355b6a9e0fa00e9b390d6b7b99e2546eac734e6f336eb5fa\" alt=\"angle B C A\"></span> and <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/bda7ab78500c35aa5c437751b3ed8239ff96d2e42967128997a709a838fa5d37\" alt=\"angle B A C\"></span>. Choice C is incorrect and may result from an error made when identifying the relationship between the exterior angle of a triangle and the interior angles of the triangle.</p><p></p>\n","correct_answer":["D"],"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 \">110</p>\n","ord":0},{"label":"B","content_html":"<p class=\"choice_paragraph \">70</p>\n","ord":1},{"label":"C","content_html":"<p class=\"choice_paragraph \">55</p>\n","ord":2},{"label":"D","content_html":"<p class=\"choice_paragraph \">40</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}}