Question

The sum of all interior angles of a regular polygon is 1080°. What is the measure of each of its interior angles? 

A. 135° 

B. 120° 

C. 156° 

D. 144°

Answer 1

The sum of interior angles of regular polygon is 

1080° = (n – 2) × 180° [n is number of sides of polygon)] 

n - 2 = 1080° / 180° 

n = 6 + 2 

= 8 

No. of Sides = 360 / Exterior Angle 

8 = 360 / Exterior Angle 

So, Exterior Angle = 360 / 8 

= 45° 

Exterior Angle + Interior Angle = 180° 

Interior Angle = 180°- 45° 

= 135°