Question

The ratio between an exterior angle and the interior angle of a regular polygon is 1: 5. Find
the measure of each interior angle

Answer 1

From the question it is given that, The ratio between an exterior angle and the interior angle of a regular polygon is 1: 5
Let us assume exterior angle be $y$ And interior angle be $5y$
We know that, sum of interior and exterior angle is equal to ${180}^{\circ }$,
$\begin{array}{c}y+5y={180}^{\circ }\\ 6y={180}^{\circ }\\ y={180}^{\circ }/6\\ y={30}^{\circ }\end{array}$
the measure of each interior angle $=5y=5\times {30}^{\circ }={150}^{\circ }$