{"id":"cb_question_bank:b954d190-3e95-4dc3-99ff-0ad88a319ecc","source_id":"cb_question_bank","source_item_id":"b954d190-3e95-4dc3-99ff-0ad88a319ecc","external_id":null,"ibn":"029403-DC","question_id":"6dd463ca","program":"SAT","module":"math","domain_code":"S","domain":"Geometry and Trigonometry","skill_code":"S.B.","skill":"Lines, angles, and triangles","difficulty":"M","score_band":4,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"In the figure above, segments AE and BD are parallel. If angle BDC measures 58° and angle ACE measures 62°, what is the measure of angle CAE ?","stimulus":"The figure presents triangle A C E, where side A E is horizontal and vertex E is to the right of vertex A. Vertex C lies above side A E. Point B lies on side A C, point D lies on side C E, and line segment B D is drawn. 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/4180fac71a78826ccc31ca2745b7a891813830705df68abb5b155da1fa1ed83a\" alt=\"The figure presents triangle A C E, where side A E is horizontal and vertex E is to the right of vertex A. Vertex C lies above side A E. Point B lies on side A C, point D lies on side C E, and line segment B D is drawn. A note states that the figure is not drawn to scale.\" width=\"143\" height=\"135\"></div>\n      </div>\n","stem_html":"<p class=\"stem_paragraph \">In the figure above, segments <span class=\"italic\">AE</span> and <span class=\"italic\">BD</span> are parallel. If angle <span class=\"italic\">BDC</span> measures 58° and angle <span class=\"italic\">ACE</span> measures 62°, what is the measure of angle <span class=\"italic\">CAE </span>?</p>\n","rationale_html":"<p>Choice B is correct. It’s given that angle <span class=\"italic\">ACE</span> measures <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/85f1617fdf48aad3a00ab977557ca5c4a13a1575e0bed765140afa14209ec89e\" alt=\"62 degrees\"></span>. Since segments <span class=\"italic\">AE</span> and <span class=\"italic\">BD</span> are parallel, angles <span class=\"italic\">BDC</span> and <span class=\"italic\">CEA</span> are congruent. Therefore, angle <span class=\"italic\">CEA</span> measures <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/3500ec445d71cc85ef1ee50ab8d682ca5fba4137f410f3e12e75e3b8bd904914\" alt=\"58 degrees\"></span>. The sum of the measures of angles <span class=\"italic\">ACE</span>, <span class=\"italic\">CEA</span>, and <span class=\"italic\">CAE</span> is <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/ec0041af7817f5d2c927cbdf134a73bc148941d5c3e5ddb80665e5fac696f97e\" alt=\"180 degrees \"></span> since the sum of the interior angles of triangle <span class=\"italic\">ACE</span> is equal to <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/ec0041af7817f5d2c927cbdf134a73bc148941d5c3e5ddb80665e5fac696f97e\" alt=\"180 degrees \"></span>. Let the measure of angle <span class=\"italic\">CAE</span> be <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/5877f887e14ac31b9a2697d829281b52cfb818895e7bd181e0390c0984a409d0\" alt=\"x degrees\"></span>. Therefore, <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/ffc7713471d0555aa0f9570bcf3d57241f59a46f4429599394c3df7953549712\" alt=\"62 plus 58, plus x, equals 180\"></span>, which simplifies to <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/b8b956f778b4b611ee95328ec27c8dfac539e57913bf6908d728efd3990938a6\" alt=\"x equals 60\"></span>. Thus, the measure of angle <span class=\"italic\">CAE</span> is <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/d42433959a799a98c6f149ec4847dd5fc9e6622bd8636d7a8a48ec2150caaac3\" alt=\"60 degrees\"></span>.</p><p>Choice A is incorrect. This is the measure of angle <span class=\"italic\">A</span><span class=\"italic\">EC</span>, not that of angle <span class=\"italic\">CAE</span>. Choice C is incorrect. This is the measure of angle <span class=\"italic\">ACE</span>, not that of <span class=\"italic\">CAE</span>. Choice D is incorrect. This is the sum of the measures of angles <span class=\"italic\">ACE</span> and <span class=\"italic\">CEA</span>.</p><p></p>\n","correct_answer":["B"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.625000+00:00","source_updated_at":"2023-08-02T20:25:59.625000+00:00","options":[{"label":"A","content_html":"<p class=\"choice_paragraph \">58°</p>\n","ord":0},{"label":"B","content_html":"<p class=\"choice_paragraph \">60°</p>\n","ord":1},{"label":"C","content_html":"<p class=\"choice_paragraph \">62°</p>\n","ord":2},{"label":"D","content_html":"<p class=\"choice_paragraph \">120°</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}}