OG详解-OG10 数学1 Q9

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°. 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 angle C. Since the sum of the measures of the interior angles of a triangle is 180°, it follows that 18°+90°+x° = 180°, or 108°+x° = 180°. Subtracting 108° from both sides of this equation yields x°= 72°. Therefore, the measure of angle C is 72°. Since angle C corresponds to angle F, it follows that the measure of angle F is also 72°.
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.