Question

The sum of interior angles of a regular polygon is thrice the sum of its exterior angles. Find the number of sides in the polygon.

Answer 1

Sum of interior angles $=3\times$ Sum of exterior angles

Let exterior angle = x

The interior angle = 3x

$\therefore x+3x={180}^o\Rightarrow x={180}^o\Rightarrow x=\frac{{180}^o}{4}={45}^o$

Number of sides $=\frac{{360}^o}{45}=8$