{"id":"cb_practice_pdf:t8-math-m2-q24","source_id":"cb_practice_pdf","source_item_id":"t8-math-m2-q24","external_id":null,"ibn":null,"question_id":null,"program":"SAT","module":"math","domain_code":null,"domain":null,"skill_code":null,"skill":null,"difficulty":null,"score_band":null,"answer_type":"mcq","answer_source":"rationale","layout_warning":"Part of this question was typeset outside the text flow — a fraction, subscript or similar — and PDF extraction re-inserted it in the wrong place. The wording is reliable; the symbols may be out of order.","form_id":"cb_practice_pdf:test-8","module_number":2,"position":24,"stem":"PQR LMN Triangles and are graphed in the PQR xy-plane. Triangle has vertices P, Q, and R at (4,5) (4,7) (6,5) LMN,, and, respectively. Triangle (4,5) (4,7+k) has vertices L, M, and N at,, (6 +k,5) and, respectively, where k is a positive ∠Q t° constant. If the measure of is, what is the ∠N measure of? (90−(t−k))°","stimulus":"","stimulus_html":null,"stem_html":"<p>PQR LMN Triangles and are graphed in the PQR xy-plane. Triangle has vertices P, Q, and R at (4,5) (4,7) (6,5) LMN,, and, respectively. Triangle (4,5) (4,7+k) has vertices L, M, and N at,, (6 +k,5) and, respectively, where k is a positive ∠Q t° constant. If the measure of is, what is the ∠N measure of? (90−(t−k))°</p>","rationale_html":"<p>= 4,5 = 4,7 Choice C is correct. Since P ^ h and Q ^ h, side PQ is parallel to the y-axis = 4,5 = 6,5 and has a length of 2. Since P ^ h and R ^ h, side PR is parallel to the x-axis and has a length of 2. Therefore, triangle PQR is a right isosceles triangle, where + 90c + + 45c P has measure and Q and R each have measure . It follows that if + c =45 = 4,5 = 4,7+ the measure of Q is t , then t . Since L ^ h and M ^ kh, side LM is + = 4,5 = 6+ ,5 parallel to the y-axis and has a length of k 2. Since L ^ h and N ^ k h, + side LN is parallel to the x-axis and has a length of k 2. Therefore, triangle LMN + 90c + + is a right isosceles triangle, where L has measure and M and N each 45c 90- c 45c have measure . Of the given choices, only ^ th is equal to , so the + 90- c measure of N is ^ th. Choice A is incorrect and may result from conceptual or calculation errors. Choice B is incorrect and may result from conceptual or calculation errors. Choice D is incorrect and may result from conceptual or calculation errors.</p>","correct_answer":["C"],"has_media":false,"has_mathml":false,"has_table":false,"source_created_at":null,"source_updated_at":null,"options":[{"label":"A","content_html":"<p>(90−(t+k))°</p>","ord":0},{"label":"B","content_html":"<p>(90−t)°</p>","ord":1},{"label":"C","content_html":"<p>(90+k)°</p>","ord":2},{"label":"D","content_html":"","ord":3}],"attribution":{"source_id":"cb_practice_pdf","source_name":"College Board full-length SAT practice tests (PDF)","rights_holder":"College Board","canonical_url":"https://satsuite.collegeboard.org/practice/practice-tests/paper","retrieved_from":"https://satsuite.collegeboard.org/practice/practice-tests/paper","attribution":"Full-length SAT practice tests 4–11 © College Board, published free at satsuite.collegeboard.org.","disclaimer":"Extracted from PDF layout: equations, figures and tables do not survive intact. Use the original PDFs for anything the text renders poorly. SAT® is a trademark registered by the College Board, which is not affiliated with and does not endorse this project.","license":"College Board copyright. Free to download; not licensed for redistribution.","redistributable":false,"item_count":905}}