Question

If the interior angle of a regular polygon is double the exterior angle, find the number of sides of polygon.

• A. 6

Answer 1

The correct option is A 6

Let exterior angle $\left(e\right)=x^{\circ }$

$\therefore$ Interior angle $\left(i\right)=2x^{\circ }$

$i+e={180}^{\circ }$

$2x+x={180}^{\circ }$

$3x={180}^{\circ }$

$x={60}^{\circ }$

$\therefore e={60}^{\circ }$

The number of sides $n=\frac{360}{e}$

$n=\frac{360}{60}$

$n=6$