Question

Difference between the interior and exterior angles of regular polygon is ${60}^{\circ }$. The number of sides in the polygon is

• A. $5$
• B. $6$
• C. $8$
• D. $9$

Answer 1

Answer: (B)

$6$

Let interior angle be $1$ and exterior angle be $E$.
We know that,
$\therefore I+E={180}^{\circ }.....\left(1\right)$
Given that,
$I-E={60}^{\circ }....\left(2\right)$
On solving $\left(1\right)$ and $\left(2\right)$, we get $I={120}^{\circ }$ and $E={60}^{\circ }$
$\therefore$ Number of sides $={360}^{\circ }/{60}^{\circ }=6$.