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*(n-2)/(n) \\ 165* n=180(n-2) \\ 165n=180n-360 \\ 165n-180n=180n-360-180n \\ -15n=-360 \\ -(15n)/(-15)=-(360)/(-15) \\ n=24 \end{gathered}`

answer: 24 sides