Question

The exterior angle of a regular polygon is one-third of its interior angle. Find the number of sides in the polygon.

Answer 1

Let interior angle = x°

Exterior angle =`1/3` x°

`therefore "x" + 1/3 "x" = 180^circ`

3x + x = 540

4x = 540

x = `540/4`

x = 135°

∴ Exterior angle = `1/3 xx 135^circ = 45^circ`

Let no.of. sides = n

∵ each exterior angle = `360^circ/"n"`

∴ 45° = `(360°)/"n"`

∴ n = `(360°)/(45°)`

n = 8