Question

In the figure below,
←→
D
F
is a straight line.

Angle D-E-F is divided into angle D-E-G measuring 3 times x plus 31 and angle G-E-F 2 times x minus 61.

What is the degree measure of
∠
F
E
G
?

A.
20
°

B.
31
°

C.
56
°

D.
124
°

Answer 1

Let m∠DEG = 3x + 31 and m∠GEF = 2x − 61. Because D–E–F is a straight line, ∠DEF is 180°, so

(3x + 31) + (2x − 61) = 180
5x − 30 = 180
5x = 210
x = 42.

Thus m∠FEG = m∠GEF = 2x − 61 = 2(42) − 61 = 84 − 61 = 23°.

So the measure is 23°, which does not appear among the given choices.