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ABC DEF Triangles and are congruent, where A corresponds to D, and B and E are right angles. The 18° measure of angle A is. What is the measure of angle F? 18°
Correct answer: B (parsed from the explanation — this source omits an answer key for this item)
Explanation
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 18° measure of angle A is . It’s also given that the measures of angles B and E are 90° . Since these angles have equal measure, they are corresponding angles. It follows that angle C corresponds to angle F. Let x° represent the measure of 180° angle C. Since the sum of the measures of the interior angles of a triangle is , 18°+90°+ °=180° 108°+ °=180° 108° it follows that x , or x . Subtracting from °=72° both sides of this equation yields x . Therefore, the measure of angle C is 72° . Since angle C corresponds to angle F, it follows that the measure of angle F 72° is also . 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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