Question

If one interior in a polygon is 140 degrees, how many sides does it have

Answer 1

`\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 =140 \end{cases}\implies n(140)=180(n-2) \\\\\\ 140n=180n-360\implies 140n+360=180n \\\\\\ 360=40n\implies \cfrac{360}{40}=n\implies 9=n`