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

Because AD ⟂ CF, ∠AGC and ∠DGF are right angles (90°). The line BE splits ∠AGC into ∠BGA and ∠BGC, each given as x + 20, so

2(x + 20) = 90 → x + 20 = 45 → x = 25.

One piece of ∠DGF is ∠DGE = 2x + 4 = 2(25) + 4 = 54°. Since ∠DGE + ∠EGF = 90°,

∠EGF = 90 − 54 = 36°.

Answer: A (36°).