Question

Find the number of sides in a regular polygon, if its interior angle is equal to its exterior angle.

Answer 1

Let $\angle ABC=x^0$ is the interior angle of the polygon.

Therefore, $ext.\angle B=x^0$ also.

$\therefore x+x={180}^{o}2x={180}^{o}x={90}^o$

Now, let no. of sides = n

$\because$ each exterior angle $=\frac{{360}^o}{n}\therefore {90}^o=\frac{{360}^o}{n}n=\frac{{360}^o}{{90}^o}=n=4$.