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 =${\displaystyle \frac{1}{3}}$ x°

${\displaystyle \therefore \text{x}+\frac{1}{3}\text{x}={180}^{\circ }}$

3x + x = 540

4x = 540

x = ${\displaystyle \frac{540}{4}}$

x = 135°

∴ Exterior angle = ${\displaystyle \frac{1}{3}\times {135}^{\circ }={45}^{\circ }}$

Let no.of. sides = n

∵ each exterior angle = ${\displaystyle \frac{{360}^{\circ }}{\text{n}}}$

∴ 45° = ${\displaystyle \frac{360°}{\text{n}}}$

∴ n = ${\displaystyle \frac{360°}{45°}}$

n = 8