Question

The interior angle of a regular polygon is double the exterior angle. The number of sides of the polygon is

• A. 8
• B. 10
• C. 6
• D. 12

Answer 1

The correct option is C

6

Let the exterior angle be $x$.
As per the given data, the interior angle is $2x$.

Now, we know the interior and exterior angle forms a linear pair.
Therefore,
$2x+x={180}^{\circ }\Rightarrow 3x={180}^{\circ }\Rightarrow x=\frac{{180}^{\circ }}{3}\Rightarrow x={60}^{\circ }$

Hence, the exterior angle is ${60}^{\circ }.$
Since the sum of all the exterior angles of a polygon is ${360}^{\circ }$, we can write
$n\times {60}^{\circ }={360}^{\circ }$, where n is the number of sides of the polygon.

$\therefore n=\frac{{360}^{\circ }}{{60}^{\circ }}=6$.

The number of sides, the polygon has is 6.