Question

For a regular polygon the sum of the interior angles is 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 $6$

Let the interior angle be $x$ and number of sides be $n$.
$\Rightarrow$ Exterior Angle $={180}^o-x$
Given: $nx=2n({180}^o-x)$
$3x={360}^o$
$x={120}^o$
We know,
$nx={180}^o(n-2)$ (Sum of interior angles of a polygon)
$60n=360$
$\therefore n=6$