Question

Find the measure of each interior angle of a regular polygon having

(i) 10 sides

(ii) 15 sides

Answer 1

In a regular polygon having 10 sides, all sides are same size and measure of all interior

Angles are

Same.

The sum of interior angles of polygon is

(n-2) × 180^o where n is the number of sides of polygon.

(10-2) × 180^o =1440 ^o here n=10

Each interior angle= 1440/10 = 144^o

(ii) In a regular polygon, all sides are same size and measure of all interior angles are

Same.

The sum of interior angles of polygon of 15 sides is

(n-2) × 180^o where n is the number of sides of polygon.

(15-2) × 180^o =1440^o here n=15

Each interior angle= 2340/15 = 156^o