# Work out the size of one interior angle of a regular 15-sided polygon?

May 28, 2018

${156}^{\circ}$

#### Explanation:

$\text{the "color(blue)"sum of the interior angles of a polygon}$ is.

•color(white)(x)180^@(n-2)

$\text{where n is the number of sides of the polygon}$

$\text{here } n = 15$

$\text{sum } = {180}^{\circ} \times 13 = {2340}^{\circ}$

$\text{one interior angle } = {2340}^{\circ} / 15 = {156}^{\circ}$