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

Triangles $ABC$ and $DEF$ are congruent, where $A$ corresponds to $D$, and $B$ and $E$ are right angles. The measure of angle $A$ is $18^{\\circ}$. What is the measure of angle $F$?

","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-40"}],"about":{"@type":"Thing","name":"Math, Geometry and Trigonometry, Duplicate"},"educationalLevel":"intermediate","eduQuestionType":"Multiple choice","learningResourceType":"Practice problem","assesses":["Math","Geometry and Trigonometry","Duplicate"],"name":"

Triangles $ABC$ and $DEF$ are congruent, where $A$ corresponds to $D$, and $B$ and $E$ are right angles. The measure of angle $A$ is $18^{\\circ}$. What is the measure of angle $F$?

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

Choice B is correct. It's given that triangle $ABC$ is congruent to triangle $DEF$. Corresponding angles of congruent triangles are congruent and, therefore, have equal measure. It's given that angle $A$ corresponds to angle $D$, and that the measure of angle $A$ is $18^{\\circ}$. It's also given that the measures of angles $B$ and $E$ are $90^{\\circ}$. Since these angles have equal measure, they are corresponding angles. It follows that angle $C$ corresponds to angle $F$. Let $x^{\\circ}$ represent the measure of angle $C$. Since the sum of the measures of the interior angles of a triangle is $180^{\\circ}$, it follows that $18^{\\circ}+90^{\\circ}+x^{\\circ}=180^{\\circ}$, or $108^{\\circ}+x^{\\circ}=180^{\\circ}$. Subtracting $108^{\\circ}$ from both sides of this equation yields $x^{\\circ}=72^{\\circ}$. Therefore, the measure of angle $C$ is $72^{\\circ}$. Since angle $C$ corresponds to angle $F$, it follows that the measure of angle $F$ is also $72^{\\circ}$.

Choice A is incorrect. This is the measure of angle $D$, not the measure of angle $F$.

Choice C is incorrect. This is the measure of angle $E$, not the measure of angle $F$.

Choice D is incorrect. This is the sum of the measures of angles $E$ and $F$, not the measure of angle $F$

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

Triangles $ABC$ and $DEF$ are congruent, where $A$ corresponds to $D$, and $B$ and $E$ are right angles. The measure of angle $A$ is $18^{\\circ}$. What is the measure of angle $F$?

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

$18^{\\circ}$

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

$90^{\\circ}$

"},{"@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":"

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

"}}},"url":"https://classnotes.xyz/mcqs/sat-math-geometry-and-trigonometry-multiple-choice-question-40"}

Triangles $ABC$ and $DEF$ are congruent, where $A$ corresponds to $D$, and $B$ and $E$ are right angles. The measure of angle $A$ is $18^{\circ}$. What is the measure of angle $F$?