Solution:
Given,
M is the center of the circle.
∠GEF = 2x° and ∠EGF = 3x°
To find:
The value of ∠FHG
Here,
- ∠EFG = 90°, being angle inscribed in a semi-circle
- ∠GEF + ∠EFG + ∠EGF = 180, being sum of the angles in a triangle.
Or, 2x° + 90° + 3x° = 180°
Or, 5x° = 180° - 90°
Or, 5x° = 90°
Or, x° = 90/5 = 18°
- ∠FHG = ∠GEF , being circumference angles of a circle standing on a same arc.
= 2x°
= 2 x 18°
= 36°
∴ The value of ∠FGH = 36°