Triangles A B C and D E F are congruent, where A corresponds to D , and B and E

Question

Triangles A B C and D E F are congruent, where A corresponds to D , and B and E are right angles. The measure of angle A is 18 &#176; . What is the measure of angle F ?

Accepted Answer

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

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