Question

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

Answer 1

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 half its adjacent interior angle, therefore, substitute $\frac{i}{2}=e$ or $i=2e$.

$e+2e={180}^0\Rightarrow 3e={180}^0\Rightarrow e=\frac{{180}^0}{3}={60}^0$

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

Here, it is given that the exterior angle is $e={60}^0$, therefore,

$n=\frac{360}{e}=\frac{360}{60}=6$

Hence, the number of sides is $6$.