The measure of angles of a hexagon are x °, ( x -5)°, ( x -5)°, (2 x -5)°, (2 x -5)°, (2 x +20)°. Find value of x.

Question

The measure of angles of a hexagon are x &#xB0;, ( x -5)&#xB0;, ( x -5)&#xB0;, (2 x -5)&#xB0;, (2 x -5)&#xB0;, (2 x +20)&#xB0;. Find value of x.

Philoid · Accepted Answer

The sum of exterior angles of interior angles of a polygon = (n – 2) × 180°

The sum of exterior angles of interior angles of a hexagon = (6 – 2) × 180° = 4 × 180° = 720°

x°+ (x-5)°+ (x-5)°+ (2x-5)°+ (2x-5)°+ (2x+20)° = 720°

x°+ x°- 5°+ x° - 5°+ 2x° - 5°+ 2x° - 5°+ 2x° + 20° = 720°

9x° = 720°

x = 80°