Question

For a regular polygon the sum of the interior anglesis twice the sum of the exterior angles, then the number of sides of the regular polygon is

• A. 4
• B. 5
• C. 6
• D. 8

Answer 1

The correct option is C 6

$\Rightarrow$ As we know sum of exterior angles of in each polygon is 360${}^{\circ }$.

$\Rightarrow$ Let $n$ be the number of angles in our polygon.

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

Since the sum of the interior angles is twice the exterior angles then,

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

$\Rightarrow$ $n-2=\frac{720}{180}$

$\Rightarrow$ $n-2=4$

$\Rightarrow$ $n=6$.