MATH SOLVE

2 months ago

Q:
# one interior angle in a regular polygon is 162° how many sides does the polygon have?

Accepted Solution

A:

[tex]\bf \textit{sum of all interior angles in a regular polygon}\\\\
S=180(n-2)\implies n\theta =180(n-2)\quad
\begin{cases}
n=\textit{number of sides}\\
\theta =\textit{interior angle}\\
----------\\
\theta =162
\end{cases}
\\\\\\
n(162) =180(n-2)\implies 162n=180n-360
\\\\\\
360=18n\implies \cfrac{360}{18}=n\implies 20=n[/tex]