{"id":"cb_question_bank:8f839359-43e3-4d01-a49e-84a634eaa3f0","source_id":"cb_question_bank","source_item_id":"8f839359-43e3-4d01-a49e-84a634eaa3f0","external_id":null,"ibn":"029285-DC","question_id":"087cdcfd","program":"SAT","module":"math","domain_code":"S","domain":"Geometry and Trigonometry","skill_code":"S.B.","skill":"Lines, angles, and triangles","difficulty":"E","score_band":1,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"In the figure, three lines intersect at point P . If x equals 65 and y equals 75 , what is the value of z ?","stimulus":"The figure presents 3 lines intersecting at point P. Six angles are formed at the point of intersection. Of the six angles, one angle is labeled x degrees, and counterclockwise angles are labeled as follows: unlabeled, y degrees, unlabeled, z degrees, and unlabeled. 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/b138f4c25e20c6f05e21575038aad241492661fffa593753f1996dd04b4e61f6\" alt=\"The figure presents 3 lines intersecting at point P. Six angles are formed at the point of intersection. Of the six angles, one angle is labeled x degrees, and counterclockwise angles are labeled as follows: unlabeled, y degrees, unlabeled, z degrees, and unlabeled. A note states that the figure is not drawn to scale.\" width=\"133\" height=\"93\"></div>\n      </div>\n","stem_html":"<p class=\"stem_paragraph \">In the figure, three lines intersect at point <span class=\"italic\">P</span>. If <span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/5a1d165abac8546e44d1b286b894dbcd1ba27a98e15e7e69e093470aabfcde27\" alt=\"x equals 65 \"></span></span> and <span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/9db75f1e4b32ed09236e8e582daa92a7e95315b319cdf817ddb81544066c4d4b\" alt=\"y equals 75\"></span></span>, what is the value of <span class=\"italic\">z </span>?</p>\n","rationale_html":"<p>Choice C is correct. The angle that is shown as lying between the <span class=\"italic\">y</span><span class=\"italic\">°</span> angle and the <span class=\"italic\">z</span><span class=\"italic\">°</span> angle is a vertical angle with the <span class=\"italic\">x</span><span class=\"italic\">°</span> angle. Since vertical angles are congruent and <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/5a1d165abac8546e44d1b286b894dbcd1ba27a98e15e7e69e093470aabfcde27\" alt=\"x equals 65\"></span>, the angle between the <span class=\"italic\">y</span><span class=\"italic\">°</span> angle and the <span class=\"italic\">z</span><span class=\"italic\">°</span> angle measures 65<span class=\"italic\">°</span>. Since the 65<span class=\"italic\">°</span> angle, the <span class=\"italic\">y</span><span class=\"italic\">°</span> angle, and the <span class=\"italic\">z</span><span class=\"italic\">°</span> angle are adjacent and form a straight angle, it follows that the sum of the measures of these three angles is 180<span class=\"italic\">°</span>, which is represented by the equation <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/25cd04b0cc11b4bd83c4512972d89cc1ce7802ca86bfea241ed42e0713acf111\" alt=\"65 degrees, plus y degrees, plus z degrees, equals 180 degrees\"></span><span class=\"italic\"></span>. It’s given that <span class=\"italic\">y</span> = 75. Substituting 75 for <span class=\"italic\">y</span> yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/c7e5cce1dbd5357c267e6add62554f23e4e902887b50169ac8d8fd9902f122a0\" alt=\"65 degrees, plus 75 degrees, plus z degrees, equals 180 degrees\"></span>, which can be rewritten as <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/3bec9b541e5728adc08fd3858dcd73ac1d9f739cb2c9ddec94923615e158fb21\" alt=\"140 degrees, plus z degrees, equals 180 degrees\"></span>. Subtracting 140<span class=\"italic\">°</span> from both sides of this equation yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/b9b58fcb89c5ff6a119099b7536d0230f20fd109cf3b844c1f79e5ffb2b56216\" alt=\"z degrees equals 40 degrees\"></span>. Therefore, <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/6ff641844a9b7f82bd6ee89680d819d19a0830b75af1f5cf682337b531a1ae11\" alt=\"z equals 40\"></span>.</p><p>Choice A is incorrect and may result from finding the value of <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/cda47c0545ab5e31a2a18321fec5f60481bc4b78af6eeb43b47e2fc0085e6be4\" alt=\"x plus y \"></span> rather than <span class=\"italic\">z</span>. Choices B and D are incorrect and may result from conceptual or computational errors.</p><p></p>\n","correct_answer":["C"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.624000+00:00","source_updated_at":"2023-08-02T20:25:59.624000+00:00","options":[{"label":"A","content_html":"<p class=\"choice_paragraph \">140</p>\n","ord":0},{"label":"B","content_html":"<p class=\"choice_paragraph \">80</p>\n","ord":1},{"label":"C","content_html":"<p class=\"choice_paragraph \">40</p>\n","ord":2},{"label":"D","content_html":"<p class=\"choice_paragraph \">20</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}}