Answer:
The measure of angle FHG is 64° ⇒ 3rd answer
Step-by-step explanation:
* Lets explain how to solve the problem
- The in-center point of a triangle is the point of intersection of the
internal angle bisectors of the triangle
- The in-center point is equidistant from the sides of the triangle
- The in-center point of a triangle is the center of the inscribed circle
of the triangle
* Lets solve the problem
∵ Point D is the in-center of triangle ABC
∴ Point D is the center of the inscribed circle in the triangle ABC
∵ D is the center of the circle
∴ ∠ FDG is a central angle subtended by arc FG
∴ ∠FHG is an inscribed angle subtended by arc FG
- The measure of the inscribed angle is half the measure of the
central angle which subtended by the same arc
∴ m∠FHG = 1/2 m∠FDG
∵ m ∠FDG = 128°
∴ m ∠FHG = 1/2 (128°) = 64°
* The measure of angle FHG is 64°
