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° $={180}^{\circ }$

$5x^{\circ }+x°={180}^{\circ }$

$6x°={180}^{\circ }$

$x°={30}^{\circ }$

$\therefore e°={30}^{\circ }$

$n=\frac{360°}{e°}$

$=\frac{360}{30}$

=12

Hence (A)