Question

Find the measures of each exterior angle of a regular Polygon of $15$ sides.

Answer 1

In a regular polygon, all sides are same size and measure of all interior angles are same.
The sum of interior angles of polygon of $15$ sides is
$(n-2)\times {180}^o$ where $n$ is number of sides of polygon.
$(15-2)\times {180}^o={1440}^o$ here $n=15$
Each interior angle $=2340/15={156}^o$
As we know that the sum of interior and exterior angles is ${180}^o$
Exterior angle + interior angle $={180}^o$
Exterior angle $+{156}^o={180}^o$
Exterior angle $={180}^o-{156}^o={24}^o$