Question

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

• A. 4
• B. 3
• C. 5
• D. 6

Answer 1

The correct option is B 3

$\Rightarrow$ Let the interior angle be $x$.

$\Rightarrow$ Then, the exterior angle will be double of it's interior angle = $2x$.

$\Rightarrow$ Then, $x+2x={180}^{\circ }$

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

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

$\therefore$ Interior angle = 60${}^{\circ }$

So, exterior angle = 120${}^{\circ }$

$n=120$

$\Rightarrow$ We know that size of an exterior angle for regular polygon = $\frac{360}{n}$

$\Rightarrow$ $\frac{360}{120}$

$\Rightarrow$ $3$

$\therefore$ The number of sides of regular polygon will be 3.