Question triang
Triangles and are congruent, where corresponds to , and and are right angles. The measure of angle is . What is the measure of angle ?
Triangles A B C and D E F are congruent, where A corresponds to D ,
Medium-difficulty · SAT Math · Lines, Angles, and Triangles — Triangle sum theorem. Read the question above, select your answer, and check the full explanation below to understand exactly why the correct choice works.
Answer explanation
Choice B is correct. It’s given that triangle is congruent to triangle . Corresponding angles of congruent triangles are congruent and, therefore, have equal measure. It’s given that angle corresponds to angle , and that the measure of angle is . It's also given that the measures of angles and are . Since these angles have equal measure, they are corresponding angles. It follows that angle corresponds to angle . Let represent the measure of angle . Since the sum of the measures of the interior angles of a triangle is , it follows that , or . Subtracting from both sides of this equation yields . Therefore, the measure of angle is . Since angle corresponds to angle , it follows that the measure of angle is also .
Choice A is incorrect. This is the measure of angle , not the measure of angle .
Choice C is incorrect. This is the measure of angle , not the measure of angle .
Choice D is incorrect. This is the sum of the measures of angles and , not the measure of angle .
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