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

Right triangles $PQR$ and $STU$ are similar, where $P$ corresponds to $S$. If the measure of angle $Q$ is $18^{\\circ}$, what is the measure of angle $S$?

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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-64"}],"about":{"@type":"Thing","name":"Math, Geometry and Trigonometry, Duplicate"},"educationalLevel":"intermediate","eduQuestionType":"Multiple choice","learningResourceType":"Practice problem","assesses":["Math","Geometry and Trigonometry","Duplicate"],"name":"

Right triangles $PQR$ and $STU$ are similar, where $P$ corresponds to $S$. If the measure of angle $Q$ is $18^{\\circ}$, what is the measure of angle $S$?

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

Choice B is correct. In similar triangles, corresponding angles are congruent. It's given that right triangles $PQR$ and $STU$ are similar, where angle $P$ corresponds to angle $S$. It follows that angle $P$ is congruent to angle $S$. In the triangles shown, angle $R$ and angle $U$ are both marked as right angles, so angle $R$ and angle $U$ are corresponding angles. It follows that angle $Q$ and angle $T$ are corresponding angles, and thus, angle $Q$ is congruent to angle $T$. It's given that the measure of angle $Q$ is $18^{\\circ}$, so the measure of angle $T$ is also $18^{\\circ}$. Angle $U$ is a right angle, so the measure of angle $U$ is $90^{\\circ}$. The sum of the measures of the interior angles of a triangle is $180^{\\circ}$. Thus, the sum of the measures of the interior angles of triangle $STU$ is $180^{\\circ}$ degrees. Let $s$ represent the measure, in degrees, of angle $S$.It follows that $s+18+90=180$, or $s+108=180$. Subtracting $108$ from both sides of this equation yields $s=72$. Therefore, if the measure of angle $Q$ is $18$ degrees, then the measure of angle $S$ is $72$ degrees.

Choice A is incorrect. This is the measure of angle $T$.

Choice C is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect. This is the sum of the measures of angle $S$ and angle $U$.

"},"encodingFormat":"text/markdown","text":"

Right triangles $PQR$ and $STU$ are similar, where $P$ corresponds to $S$. If the measure of angle $Q$ is $18^{\\circ}$, what is the measure of angle $S$?

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

$18^{\\circ}$

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

$82^{\\circ}$

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

$162^{\\circ}$

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

$72^{\\circ}$

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

Choice A is incorrect. This is the measure of angle $T$.

Choice C is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect. This is the sum of the measures of angle $S$ and angle $U$.

"},"answerExplanation":{"@type":"Comment","text":"

Choice A is incorrect. This is the measure of angle $T$.

Choice C is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect. This is the sum of the measures of angle $S$ and angle $U$.

"}}},"url":"https://classnotes.xyz/mcqs/sat-math-geometry-and-trigonometry-multiple-choice-question-64"}

Right triangles $PQR$ and $STU$ are similar, where $P$ corresponds to $S$. If the measure of angle $Q$ is $18^{\circ}$, what is the measure of angle $S$?