Question

The measure of each interior angle of a regular polygon is five times the measure of its exterior angle. Find:

$\left(ii\right)$ Measure of each exterior angle.

Answer 1

Step: Finding the measure of each exterior angle

Let, each exterior angle $=x.$

Then, each interior angle $=5x$.

We know, Interior angle + exterior angle $={180}^{\circ }$

$\Rightarrow 5x+x={180}^{\circ }$

$\Rightarrow 6x={180}^{\circ }$

$\Rightarrow x=\frac{{180}^{\circ }}{6}$

$\Rightarrow x={30}^{\circ }$

Thus, each interior angle $=5\left({30}^{\circ }\right)={150}^{\circ }$

And each exterior angle $=x={30}^{\circ }$

Hence, each exterior angle measure is ${30}^{\circ }$.