Question

G is the incenter, or point of concurrency, of the angle bisectors of ΔACE.

Triangle A C E has point G as its incenter. Lines are drawn from the points of the triangle to point G. Lines are drawn from point G to the sides of the triangle to form right angles. Line segments G B, G D, and G F are formed. Angle F E G is (3 n minus 1) degrees and angle D E G is 20 degrees.
What is the value of n?

6
7
20
59

Answer 1

G is the incenter, so EG bisects angle AEC. Therefore ∠FEG = ∠DEG, so

3n − 1 = 20
3n = 21
n = 7.

Answer: 7.