Question

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

Answer 1

Step: Find the number of sides of the polygon.

Given, sum of interior angles = 2 (sum of exterior angles)

Let number of sides $=n$.

Then, Sum of interior angle $=(n-2)\times {180}^{\circ }$
and sum of exterior angle $={360}^{\circ }$

$\Rightarrow (n-2)\times {180}^{\circ }=2\times {360}^{\circ }$

$\Rightarrow n-2=\frac{2\times {360}^{\circ }}{{180}^{\circ }}$

$\Rightarrow n-2=2\times 2$

​​​​​​​$\Rightarrow n-2=4$

$\Rightarrow n=6$

​​​​​​​Hence, number of sides of the polygon is 6.