Question

If UVW is congruent to EFC, what is the measure of ∠CFE?

A) 30°
B) 60°
C) 90°
D) 120°

Answer 1

If UVW is congruent to EFC, the measure of angle CFE is 60°.

Step-by-step explanation:

Given that UVW is congruent to EFC, we can conclude that the corresponding angles in these triangles are congruent as well. Therefore, angle U is congruent to angle E, angle V is congruent to angle F, and angle W is congruent to angle C. Since the sum of the angles in a triangle is always 180 degrees, we can determine the measure of angle CFE by subtracting the measures of angles V and F from 180 degrees.

Let's assume that angle V has a measure of x degrees. Then, angle F also has a measure of x degrees. Angle C is congruent to angle W, which is also congruent to angle V. Therefore, angle C has a measure of x degrees as well. From the information given, we know that angle V + angle F + angle C = 180 degrees. Substituting x for the measures of angles V, F, and C, we get:

x + x + x = 180 degrees
3x = 180 degrees
x = 60 degrees

Therefore, the measure of angle CFE (angle F) is 60 degrees, which is option B.