{"id":"cb_question_bank:191426f9-1f46-4e21-99db-fbcbeee648dd","source_id":"cb_question_bank","source_item_id":"191426f9-1f46-4e21-99db-fbcbeee648dd","external_id":null,"ibn":"019566-DC","question_id":"a6dbad6b","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":"The figure presents 2 parallel lines l and m, which are almost horizontal, with l above m. A line segment from the left on m, moves up and to the right, intersects, and ends above l. Another line segment from the right on m, moves up and to the left, intersects, and ends at the same point as the other line segment, above l. The angle at the point where the two line segments meet is labeled x degrees. The angle above l and to the left of the right line segment is labeled z degrees. The angle above m and to the right of the left line segment is labeled y degrees. The figure is not drawn to scale In the figure above, lines l and m are parallel, y equals 20 , and z equals 60 . What is the value of x ?","stimulus":"","stimulus_html":"<div class=\"stimulus_reference \">\n            <div class=\"standalone_image \"></div>\n          </div>\n","stem_html":"<p><img src=\"/api/assets/e040af30e9bb8e4ec6b00a4d1e439583d2cc2b6fc150f730389865fb39670acc\" alt=\"The figure presents 2 parallel lines l and m, which are almost horizontal, with l above m. A line segment from the left on m, moves up and to the right, intersects, and ends above l. Another line segment from the right on m, moves up and to the left, intersects, and ends at the same point as the other line segment, above l. The angle at the point where the two line segments meet is labeled x degrees. The angle above l and to the left of the right line segment is labeled z degrees. The angle above m and to the right of the left line segment is labeled y degrees. The figure is not drawn to scale\" width=\"193\" height=\"101\"></p><p class=\"stem_paragraph \">In the figure above, lines <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/b3ed61300b239762a0f7bec1dc9a48ecd5e011d08d5338f426429aa3c459a067\" alt=\"l\"></span><span class=\"italic\"></span> and <span class=\"italic\">m</span> are parallel, <span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/534f21cb3018d9fe80617626c575ab8679a1cc4d6e2e8676103e3bd0562e26f8\" alt=\"y equals 20\"></span></span>, and <span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/478d3b0d5dbbdd10cb7129999c5dc213686b6c386b78779422a7a3a99744abc1\" alt=\"z equals 60\"></span></span>. What is the value of <span class=\"italic\">x</span> ?</p><p></p>\n","rationale_html":"<p>Choice B is correct. Let the measure of the third angle in the smaller triangle be <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/3c1041213affdf47e48a7994b7504554536770a6f9a287d55d562a79bd2a2cc7\" alt=\"a, degrees\"></span>. Since lines <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/b3ed61300b239762a0f7bec1dc9a48ecd5e011d08d5338f426429aa3c459a067\" alt=\"l\"></span> and <span class=\"italic\">m</span> are parallel and cut by transversals, it follows that the corresponding angles formed are congruent. So <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/4e422ba7c8a2db100422c88aaaf63bb31203bc506aafb9bc1f529639d6a3468c\" alt=\"a degrees, equals y degrees, which equals 20 degrees\"></span>. The sum of the measures of the interior angles of a triangle is <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/ec0041af7817f5d2c927cbdf134a73bc148941d5c3e5ddb80665e5fac696f97e\" alt=\"180 degrees\"></span>, which for the interior angles in the smaller triangle yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/678e85fab52f95a6a28c72cb9a288caa0822e3d3932f03f8db4618ccef0e4dca\" alt=\"a, plus x, plus z, equals 180\"></span>. Given that <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/478d3b0d5dbbdd10cb7129999c5dc213686b6c386b78779422a7a3a99744abc1\" alt=\"z equals 60\"></span> and <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/8c0cfac6c0bfac5412628d606b7d790416af75ede5eb361bb18208eb9e416429\" alt=\"a, equals 20\"></span>, it follows that <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/5a98b51be474125ad37a3b68a5220d318cc9942d601dc973ed8a7e6a54110847\" alt=\"20 plus x, plus 60, equals 180\"></span>. Solving for <span class=\"italic\">x</span> gives <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/5ed0138b860f1de4453ce662e5766da95bbb63b8b1267695ff549e204f57e483\" alt=\"x equals, 180 minus 60, minus 20\"></span>, or <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/e89a11a5938631839440ee70e628fad11515b238437b8f95c02c75b11dca3ea5\" alt=\"x equals 100\"></span>.</p><p>Choice A is incorrect and may result from incorrectly assuming that angles <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/64f87df36b9185d7f2050a1067fef482d94923c092a3325355de82e8c141efb3\" alt=\"x plus z, equals 180\"></span>. Choice C is incorrect and may result from incorrectly assuming that the smaller triangle is a right triangle, with <span class=\"italic\">x</span> as the right angle. Choice D is incorrect and may result from a misunderstanding of the exterior angle theorem and incorrectly assuming that <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/39e42ac1650dc992776140d1ab937e39a2a79a83201744824a6c0c084ab7dbfd\" alt=\"x equals, y plus z\"></span>.</p><p></p>\n","correct_answer":["B"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.616000+00:00","source_updated_at":"2023-08-02T20:25:59.616000+00:00","options":[{"label":"A","content_html":"<p>120</p>\n","ord":0},{"label":"B","content_html":"<p>100</p>\n","ord":1},{"label":"C","content_html":"<p>90</p>\n","ord":2},{"label":"D","content_html":"<p>80</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}}