Question

The exterior angle of a regular polygon is one – third of its interior angle. How many sides has the polygon?

• A. Nonagon
• B. Decagon
• C. Octagon
• D. None of these

Answer 1

The correct option is C

Octagon

Each interior angle of a polygon$=\left\{\frac{(2n-4)}{n}\right\}\times {90}^{\circ }$

Each exterior angle of a polygon $=\frac{{360}^{\circ }}{n}$

As per question,

$\frac{1}{3}\left\{\frac{(2n-4)}{n}\right\}\times {90}^{\circ }=\frac{{360}^{\circ }}{n}$

$\frac{1}{3}\left\{\frac{(2n-4)}{n}\right\}=\frac{4}{n}$

2n = 16

n = 8

So, the polygon is octagon.