Question

Find the number of sides of a polygon whose exterior and interior angles are in the ratio 1 : 5.

• A. 10
• B. 15
• C. 12
• D. 14

Answer 1

The correct option is C 12

Let the number of sides of polygon = $n$

Measure of exterior angle $=x^{\circ }$
Measure of interior angle $=5x^{\circ }$

Sum of exterior angle + interior angle is ${180}^{\circ }$.
$\Rightarrow x^{\circ }+5x^{\circ }={180}^{\circ }$
$\Rightarrow 6x={180}^{\circ }$
$\Rightarrow x={30}^{\circ }$

Sum of all exterior angles $={360}^{\circ }$
$\Rightarrow {30}^{\circ }\times n={360}^{\circ }$
Hence, n = 12

$\therefore$ Number of sides of the required polygon = 12