Answer:
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°
