The angle bisectors of AXYZ are XG, YG, and ZG. They meet at a single point G. (In other words, G is the incenter of AXYZ.)
Suppose DG= 10, ZG= 19, mŁ DYE =96°, and m2 FXG=18°.
Find the following measures.
Note that the figure is not drawn to scale.

m∠FXD = 36°

EG = 10

m∠FZG = 24°

Step-by-step explanation:

In triangle XYZ, G is the incenter of the triangle.

Since, m∠FXG = 18°

And m∠FXD = 2(m∠FXG)

                     = 2 × 18°

                     = 36°

Since, point G is equidistant from all sides (Property of incenter of a triangle)

Therefore, DG = EG = GF = 10

Since, m∠X + m∠Y + m∠Z = 180°

2(m∠FXG) + m∠DYE + 2(m∠FZG) = 180°

2(18)° + 96° + 2(m∠FZG) = 180°

2(m∠FZG) = 180° - 132°

m∠FZG = 24°

rotated. i took the test

step-by-step explanation:

you can't solve x because it is 2 linear equation and you only have one equation