Question

In a regular polygon, the ratio of the interior angle to the corresponding exterior angle is 11 : 7. What is the measure of the interior angle?

Answer 1

Given : Ratio of interior angle to the corresponding exterior angle = 11 : 7

We know that sum of interior angle to the corresponding exterior angle is equal to ${180}^{\circ }$.

So, we need to divide ${180}^{\circ }$ in 11 + 7 = 18 parts.$\left[1mark\right]$

Measure of each part = $\frac{{180}^{\circ }}{18}={10}^{\circ }$

$\therefore$ Measure of interior angle
= 11 $\times$ Measure of each part = ${110}^{\circ }$$\left[1mark\right]$