{"@context":"https://schema.org/","@type":"Quiz","name":"

In the figure below, lines $l$ and $m$ are parallel, $y=20$, and $z=60$. What is the value of $x$?

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","hasPart":{"@type":"Question","typicalAgeRange":"12-22","educationalAlignment":[{"@type":"AlignmentObject","alignmentType":"educationalSubject","targetName":"SAT"},{"@type":"AlignmentObject","alignmentType":"educationalLevel","targetName":"SAT","educationalFramework":"Common Core","targetUrl":"https://classnotes.xyz/mcqs/sat-math-geometry-and-trigonometry-multiple-choice-question-65"}],"about":{"@type":"Thing","name":"Math, Geometry and Trigonometry, Duplicate"},"educationalLevel":"intermediate","eduQuestionType":"Multiple choice","learningResourceType":"Practice problem","assesses":["Math","Geometry and Trigonometry","Duplicate"],"name":"

In the figure below, lines $l$ and $m$ are parallel, $y=20$, and $z=60$. What is the value of $x$?

$\"\"$

","comment":{"@type":"Comment","text":"

Choice B is correct. Let the measure of the third angle in the smaller triangle be $a^{\\circ}$. Since lines $l$ and $m$ are parallel and cut by transversals, it follows that the corresponding angles formed are congruent. So $a^{\\circ}=y^{\\circ}=20^{\\circ}$. The sum of the measures of the interior angles of a triangle is $180^{\\circ}$, which for the interior angles in the smaller triangle yields $a+x+z=180$. Given that $z=60$ and $a=20$, it follows that $20+x+60=180$. Solving for $x$ gives $x=180-60-20$, or $x=100$.

Choice A is incorrect and may result from incorrectly assuming that angles $x+z=180$. Choice C is incorrect and may result from incorrectly assuming that the smaller triangle is a right triangle, with $x$ as the right angle. Choice D is incorrect and may result from a misunderstanding of the exterior angle theorem and incorrectly assuming that $x=y+z$.

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In the figure below, lines $l$ and $m$ are parallel, $y=20$, and $z=60$. What is the value of $x$?

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","suggestedAnswer":[{"@type":"Answer","position":0,"encodingFormat":"text/html","text":"

120

"},{"@type":"Answer","position":2,"encodingFormat":"text/html","text":"

"},{"@type":"Answer","position":3,"encodingFormat":"text/html","text":"

"}],"acceptedAnswer":{"@type":"Answer","position":1,"encodingFormat":"text/html","text":"

100

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