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 $=x^o$

$\therefore$ Exterior angle $=\frac{1}{3}{x}^o$

$\therefore x+\frac{1}{3}x={180}^{o}3x+x=5404x=540x=\frac{540}{4}x={135}^o$

$\therefore Exteriorangle=\frac{1}{3}\times {135}^o={45}^o$

Let no. of sides = n

$\because$ each exterior angle $=\frac{{360}^o}{n}\therefore {45}^o=\frac{{360}^o}{n}\therefore n=\frac{{360}^o}{{45}^o}n=8$.