Question

The exterior angle of a polygon is one-sixth of it's interior angle. What are the angles?

Answer 1

Let the interior angle be $x$.

$\therefore$ Exterior angle $=\frac{1}{6}x$

We know that,

Interior angle $+$ Exterior angle $={180}^{\circ }$

$\therefore x+\frac{1}{6}x={180}^{\circ }$

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

$\Rightarrow \frac{7x}{6}={180}^{\circ }$

$\therefore x={180}^{\circ }\times \frac{6}{7}={154.3}^{\circ }$

Thus, exterior angle $={154.3}^{\circ }÷6={25.7}^{\circ }$