Question

Determine the number of sides the polygon for which the ratio of the sum of the interior angles to the sum of the exterior angle is 5: 1.

Answer 1

Suppose number of sides be $n,$ then
$\frac{\text{sum of interior angles}}{\text{sum of exterior angles}}=\frac{5}{1}$
$\Rightarrow \frac{(2n-4)\times {90}^{\circ }}{{360}^{\circ }}=\frac{5}{1}$
$\Rightarrow 2n-4=20$
$\Rightarrow n=12$