Question

If an exterior angle of a regular polygon is equal to its an interior angle, find the number of sides in the polygon.

Answer 1

Let interior angle and exterior angle of a polygon be $x$.

Interior angle $+$ Exterior angle $={180}^o.$

$\Rightarrow$ $x+x={180}^o$

$\Rightarrow$ $2x={180}^o$

$\Rightarrow$ $x={90}^o.$

$\therefore$ Exterior angle $={90}^o.$

$\Rightarrow$ Number of sides $=\frac{{360}^o}{Exteriorangle}$

$=\frac{{360}^o}{{90}^o}$

$=4$

$\therefore$ The number of sides of a polygon is $4.$