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Work out the number of sides of a regular polygon with interior angle 177
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Work out the number of sides of a regular polygon with interior angle 177

User Sudheer Jami
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\underset{in~degrees}{\textit{sum of all interior angles}}\\\\ n\theta = 180(n-2) ~~ \begin{cases} n=\stackrel{number~of}{sides}\\ \theta = \stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ \theta =177 \end{cases}\implies n(177)=180n-360 \\\\\\ 177n=180n-360\implies 0=3n-360\implies 360=3n \\\\\\ \cfrac{360}{3}=n\implies 120=n

User Bscothern
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