Question

Find the number of sides of a regular polygon, if the exterior angle is one-ninth of its interior angle?

Answer 1

let interior angle be x and exterior angle be y
so, x + y = 180°.............(1)

the exterior angle is one-ninth of its interior angle
so, y = x/9.............(2)

substitute (2) in (1)
x + x/9 = 180°
(9x + x)/9 = 180°
10x = 180° × 9
x = 18° × 9
x = 162°

so, interior angle is x = 162°

exterior angle is y = 180° - 162° = 18°

so, no of sides of polygon = 360°/18° = 20

no of sides of a polygon is 20