Question

The ratio between the interior angle and the exterior angle of a regular polygon is $2:1$ find each exterior angle of the polygon

• A. ${60}^{\circ }$
• B. ${50}^{\circ }$
• C. ${40}^{\circ }$
• D. ${45}^{\circ }$

Answer 1

The correct option is A ${60}^{\circ }$

The ratio between the interior angle and the exterior angle of a regular polygon is $2:1$.

Each interior angle of a regular polygon $=\frac{{180}^o(n-2)}{n}$ where $n=$ number of sides of polygon

Each exterior angle of a regular polygon $=\frac{{360}^o}{n}$

According to question,

$\frac{{180}^o(n-2)}{n}:\frac{{360}^o}{n}=2:1$

$=>\frac{(n-2)}{2}=\frac{2}{1}$

$=>n-2=4$

$=>n=6$

Each exterior angle of a regular polygon $=\frac{{360}^o}{n}=\frac{{360}^o}{6}={60}^o$