Question

If in a regular polygon, each exterior angle is twice the interior angle, then the number of sides will be:

• A. $4$
• B. $5$
• C. $3$
• D. $6$

Answer 1

The correct option is C $3$

Let there be n sides, then sum of interior angles$=(n-2)180$

Each interior angle will be $=\frac{n-2}{n}\left(180\right)$

Each exterior angle will be $=\left(2\right)$$\left(\frac{n-2}{n}\right)\times 180$

Thus, $\frac{n-2}{n}\left(180\right)$ + (2) $\left(\frac{n-2}{n}\right)\times 180$ = 180

$\frac{n-2}{n}\left(3\right)=1$

$3n-6=n$

$n=3$