{"id":"cb_question_bank:d64201b2-a2f3-47de-93b1-d6addced5e39","source_id":"cb_question_bank","source_item_id":"d64201b2-a2f3-47de-93b1-d6addced5e39","external_id":null,"ibn":"08194-DC","question_id":"3828f53d","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, lines m and n are parallel. What is the value of b ?","stimulus":"The figure presents 5 lines labeled j, k, l, m, and n. Lines m and n are horizontal and line m lies above line n. Line j is slanted downward and to the right, and line k is slanted upward and to the right. Lines j, k, and top horizontal line m intersect, forming six angles. The angle below line m and to the left of line k and the angle below line m and to the right of line j are both labeled, a, degrees. Line k intersects the bottom horizontal line n, forming four angles. The angle above line n and to the left of line k is labeled 130 degrees. Line l is vertical and intersects lines m and n on the right side of the figure. Line j, line l, and the bottom horizontal line n intersect, forming six angles. The angle, above line n, to the left of vertical line l, and to the right of line j is labeled b degrees. There is a right angle symbol at an angle formed by horizontal line m and vertical line l.","stimulus_html":"<div class=\"stimulus_reference \">\n          <div class=\"standalone_image \">\n            <img src=\"/api/assets/4eb2633b301c314ec2ad25100c9d76dac3d081cf97e7af34963cf83c5cdac9d3\" alt=\"The figure presents 5 lines labeled j, k, l, m, and n. Lines m and n are horizontal and line m lies above line n. Line j is slanted downward and to the right, and line k is slanted upward and to the right. Lines j, k, and top horizontal line m intersect, forming six angles. The angle below line m and to the left of line k and the angle below line m and to the right of line j are both labeled, a, degrees. Line k intersects the bottom horizontal line n, forming four angles. The angle above line n and to the left of line k is labeled 130 degrees. Line l is vertical and intersects lines m and n on the right side of the figure. Line j, line l, and the bottom horizontal line n intersect, forming six angles. The angle, above line n, to the left of vertical line l, and to the right of line j is labeled b degrees. There is a right angle symbol at an angle formed by horizontal line m and vertical line l.\" width=\"139\" height=\"107\"></div>\n        </div>\n","stem_html":"<p class=\"stem_paragraph \">In the figure above, lines <span class=\"italic\">m</span> and <span class=\"italic\">n</span> are parallel. What is the value of <span class=\"italic\">b</span> ?</p>\n","rationale_html":"<p>Choice A is correct. Given that&nbsp;lines <span class=\"italic\">m</span> and <span class=\"italic\">n</span> are parallel, the angle marked 130° must be supplementary to the leftmost&nbsp;angle marked&nbsp;<span class=\"italic\">a</span>° because they are same-side interior angles. Therefore, 130° + <span class=\"italic\">a°</span> = 180°, which yields&nbsp;<span class=\"italic\">a</span> = 50°. 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>&nbsp;intersect at a right angle, so lines <span class=\"italic\">j</span>, <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> form a right triangle where the two acute angles are <span class=\"italic\">a</span>° and <span class=\"italic\">b</span>°. The acute angles of a right triangle are complementary, so <span class=\"italic\">a°</span> + <span class=\"italic\">b°</span> = 90°, which yields 50° + <span class=\"italic\">b°</span> = 90°, and&nbsp;<span class=\"italic\">b</span> = 40.</p><p>Choice B is incorrect. This is the value of <span class=\"italic\">a</span>, not <span class=\"italic\">b</span>. Choice C is incorrect and may be the result of&nbsp;dividing 130°&nbsp;by 2. Choice D is incorrect and may be the result of multiplying <span class=\"italic\">b</span> by 2.<span class=\"italic\"></span></p><p></p>\n","correct_answer":["A"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.635000+00:00","source_updated_at":"2023-08-02T20:25:59.635000+00:00","options":[{"label":"A","content_html":"<p class=\"choice_paragraph \">40</p>\n","ord":0},{"label":"B","content_html":"<p class=\"choice_paragraph \">50</p>\n","ord":1},{"label":"C","content_html":"<p class=\"choice_paragraph \">65</p>\n","ord":2},{"label":"D","content_html":"<p class=\"choice_paragraph \">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}}