Question

The ratio between the exterior angle and the interior angle of a regular polygon is 1:5, then it has___ sides.

• A. 12
• B. 10
• C. 8
• D. 6

Answer 1

The correct option is A

12

Let the exterior angle $=x^{\circ }$ and interior angle $=5x^{\circ }$

We know that $i+e={180}^{\circ }$

$5x^{\circ }+x={180}^{\circ }$

$6x={180}^{\circ }$

$x={30}^{\circ }$

$\therefore e={30}^{\circ }$

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

$\Rightarrow n=\frac{360}{30}$

$\Rightarrow n=12$

Hence (A)