Question

Find the number of sides of a regular polygon if each exterior angle is equal to its adjacent interior angle

Answer 1

Let $e$ be the exterior angle and $i$ be the interior adjacent angle of a regular polygon.

The sum of exterior angle and its adjacent interior is ${180}^0$, that is,

$e+i={180}^0$

Since each exterior angle is equal to its adjacent interior angle, therefore, substitute $i=e$

$e+e={180}^0$

$\Rightarrow 2e={180}^0$

$\Rightarrow e=\frac{180}{2}={90}^0$

We know that the measure of exterior angle is $e={\left(\frac{360}{n}\right)}^0$ where $n$ is the number of sides of a polygon.

Here, it is given that the exterior angle is $e={90}^0$, therefore,

$n=\frac{360}{e}$

$=\frac{360}{90}$

$=4$

Hence, the number of sides is $4$.