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One interior angle in a regular polygon is 162° how many sides does the polygon have?
4 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]