Question

Given the measure of one interior angle of a REGULAR n-gon is 165 degrees, find the number of sides

Answer 1

the formula is

$\begin{gathered} 165=180\times\frac{n-2}{n} \\ 165\times n=180(n-2) \\ 165n=180n-360 \\ 165n-180n=180n-360-180n \\ -15n=-360 \\ -\frac{15n}{-15}=-\frac{360}{-15} \\ n=24 \end{gathered}$

answer: 24 sides