{"id":"cb_question_bank:6bd50b59-5866-4006-87c4-e87ff0bedc6b","source_id":"cb_question_bank","source_item_id":"6bd50b59-5866-4006-87c4-e87ff0bedc6b","external_id":null,"ibn":"022230-DC","question_id":"dfc420b2","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 figure above, line segment A, D intersects line segment B E at C . If x equals 100 , what is the value of y ?","stimulus":"The figure presents line segments A, D and B E intersecting at point C. Line segments A, B and D E together with line segments A, D and B E form two triangles, A, B C and C D E. In triangle A, B C, angle A, measures 20 degrees, angle B measures x degrees, and the measure of angle C is not given. In triangle C D E, angle D measures y degrees, angle E measures 40 degrees, and the measure of angle C is not given. Angle C of triangle A, B C appears to be congruent to angle C of triangle C D E. A note states that the figure is not drawn to scale.","stimulus_html":"<div class=\"stimulus_reference \">\n        <div class=\"standalone_image \">\n          <img src=\"/api/assets/e12b8a9df483e65eb813a3ee794b628cb12c420433886fb513a38c56cc2effd2\" alt=\"The figure presents line segments A, D and B E intersecting at point C. Line segments A, B and D E together with line segments A, D and B E form two triangles, A, B C and C D E.  In triangle A, B C, angle A, measures 20 degrees, angle B measures x degrees, and the measure of angle C is not given. In triangle C D E, angle D measures y degrees, angle E measures 40 degrees, and the measure of angle C is not given. Angle C of triangle A, B C appears to be congruent to angle C of triangle C D E. A note states that the figure is not drawn to scale.\" width=\"183\" height=\"121\"></div>\n      </div>\n","stem_html":"<p class=\"stem_paragraph \">In the figure above, <span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/5705778c8b1db5417d63233727ccd486185728f6c5591e8b34aec5446b344b81\" alt=\"line segment A, D\"></span></span> intersects <span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/8313a0f8199634f3a6b30d6a003dcc9be420cfbba72995f3ce51b6dc34b49f5d\" alt=\"line segment B E\"></span></span> at <span class=\"italic\">C</span>. If <span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/e89a11a5938631839440ee70e628fad11515b238437b8f95c02c75b11dca3ea5\" alt=\"x equals 100\"></span></span>, what is the value of <span class=\"italic\">y</span> ?</p>\n","rationale_html":"<p>Choice C is correct. It’s given that <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/e89a11a5938631839440ee70e628fad11515b238437b8f95c02c75b11dca3ea5\" alt=\"x equals 100\"></span>; therefore, substituting 100 for <span class=\"italic\">x</span> in triangle <span class=\"italic\">ABC</span> gives two known angle measures for this triangle. The sum of the measures of the interior angles of any triangle equals 180°. Subtracting the two known angle measures of triangle <span class=\"italic\">ABC</span> from 180° gives the third angle measure: <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/34bff8655a6d7591b2f0616101818d32c7c57cf94a308632ed15cbf7af93a992\" alt=\"180 degrees minus 100 degrees, minus 20 degrees, equals 60 degrees\"></span>. This is the measure of angle <span class=\"italic\">BCA</span>. Since vertical angles are congruent, the measure of angle <span class=\"italic\">DCE</span> is also 60°. Subtracting the two known angle measures of triangle <span class=\"italic\">CDE</span> from 180° gives the third angle measure: <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/5dad04312156998b8ff03889981263885f046277a5165f331a4ce1870475d678\" alt=\"180 degrees minus 60 degrees, minus 40 degrees, equals 80 degrees\"></span>. Therefore, the value of <span class=\"italic\">y</span> is 80.</p><p>Choice A is incorrect and may result from a calculation error. Choice B is incorrect and may result from classifying angle <span class=\"italic\">CDE</span> as a right angle. Choice D is incorrect and may result from finding the measure of angle <span class=\"italic\">BCA</span> or <span class=\"italic\">DCE</span> instead of the measure of angle <span class=\"italic\">CDE</span>.</p><p></p>\n","correct_answer":["C"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.617000+00:00","source_updated_at":"2023-08-02T20:25:59.617000+00:00","options":[{"label":"A","content_html":"<p class=\"choice_paragraph \">100</p>\n","ord":0},{"label":"B","content_html":"<p class=\"choice_paragraph \">90</p>\n","ord":1},{"label":"C","content_html":"<p class=\"choice_paragraph \">80</p>\n","ord":2},{"label":"D","content_html":"<p class=\"choice_paragraph \">60</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}}