Question

In the diagram below,
←→
A
D
,
←→
B
E
, and
←→
C
F
intersect at point G.

Line A-D is perpendicular to line C-F. Angle A-G-C is divided into angles B-G-C and B-G-A measuring x plus 20. Angle D-G-F is divided into angles D-G-E and angle E-G-F measuring 2 times x plus 4.

What is the measure of
∠
F
G
E
?

A.
36
°

B.
48
°

C.
52
°

D.
108
°

Answer 1

Answer: A (36°)

Reason: Rays GB and GE are opposite (they lie on line BE) and rays GC and GF are opposite (they lie on line CF), so ∠BGC and ∠EGF are vertical angles and therefore equal. Thus

x + 20 = 2x + 4
=> x = 16.

Then ∠FGE = ∠EGF = 2x + 4 = 2(16) + 4 = 36°.