Question

Point G is the incenter of the triangle.

Point G is the incenter of triangle E D F. Lines are drawn from each point of the triangle to point G. Lines are drawn from point G to the sides of the triangle. Angle D F G is 16 degrees. Angle G F E is (2 x) degrees.
What is the value of x?

4
8
24
32

Answer 1

G is the incenter, so FG bisects angle EFD. Therefore angle DFG = angle GFE. Given DFG = 16° and GFE = 2x, we have 2x = 16, so x = 8.