Question

Part A

What is the value of x?



Part B


Which explanation best describes the correct measure of AFE?


A. Substitute the value of x to find the measure of AFC. Then subtract the total from 180° because AFC and AFE are supplementary.

B. Substitute the value of x to find the measure of AFC. Then subtract the total from 180° because AFC and AFE
are supplementary.

C. Substitute the value for x to find the measure of CFD. This is equal to the measure of AFE because CFD and AFE are vertical angles.

D. Substitute the value for x to find the sum of the measures of AFB and BFC. Then subtract the sum of 90° because AFC and AFE are complementary.

E. Substitute the value for x to find the sum of measures of AFB and BFC. The sum of the measures of AFB and BFC is equal to the measure of AFE because the angles are adjacent angles.

Answer 1

C

Explanation:

∠ AFD = ∠ AFB + ∠ BFC + ∠ CFD

The 3 angles form a straight angle and sum to 180°, that is

4x + 5 + 6x + 3 + 5x + 7 = 180, that is

15x + 15 = 180 ( subtract 15 from both sides )

15x = 165 ( divide both sides by 15 )

x = 11

∠ CFD = 5x + 7 = 5(11) + 7 = 55 + 7 = 62°, thus

∠ AFE = ∠ CFD = 62° ( vertical angles are congruent )