Question

If the interior angle of a regular polygon is double the exterior angle then the polygon is ___

• A. Triangle
• B. Pentagon
• C. Hexagon
• D. Octagon

Answer 1

The correct option is C

Hexagon

It is given that the polygon is regular. So all the sides and angles of the polygon are equal.

Let exterior angle = e° $\Rightarrow$ Interior angle = 2e°

In a polygon, the sum of an interior angle and its respective exterior angle is 180°

$\Rightarrow$ interior angle + exterior angle = 180°

$\Rightarrow$ 2e + e = 180°

$\Rightarrow$ 3e = 180°

$\Rightarrow$ e = 60°

$\therefore$ exterior angle = 60°

$\because$ Sum of exterior angles of any polygon = 360${}^{\circ }$

$\Rightarrow$ n $\times$ exterior angle = 360${}^{\circ }$ (where, n= Number of sides)

$\Rightarrow$ n =$\frac{360°}{\text{exterior angle}}$

= $\frac{360°}{60°}$

= 6

$\because$ Number of sides of polygon is 6, so the given polygon is hexagon.