Question

The ratio between an exterior angle and an interior angle of a polygon is $2:3$. Find the number of sides in the polygon.

Answer 1

Let the exterior angle be $2x$

and interior angle be $3x$

summation of exterior angle and interior angle is ${180}^0$

$\Rightarrow 2x+3x=180\Rightarrow 5x=180\Rightarrow x=36$

so exterior angle $2x$=${72}^0$

summation of all exterior angle of a polygon is ${360}^0$

let number of sides of polygon be $n$

so $72\times n=360$

$\Rightarrow n=\frac{360}{72}\Rightarrow n=5$