Problem — Interior angle of a regular 15-gon

Text

A regular polygon (that is, equilateral and equiangular) has $15$ sides. Compute the measure of one of its interior angles.

Solution

The sum of the interior angles of a convex polygon with $n$ sides equals $(n-2)\cdot 180^\circ$. For $n = 15$: $(15 - 2)\cdot 180^\circ = 13 \cdot 180^\circ = 2340^\circ.$ In a regular polygon the $15$ interior angles are all congruent, so each one measures $\frac{2340^\circ}{15} = 156^\circ.$ $\boxed{\widehat{\text{interior}} = 156^\circ}$