Find the measures of an exterior angle and an interior angle given a regular polygon with 7 sides. Round to the nearest tenth, if necessary.
[tex]\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\\ n=7 \end{cases}\implies 7\theta =180(7-2) \\\\\\ 7\theta =900\implies \theta =\cfrac{900}{7}\implies \theta =128\frac{4}{7}\implies \theta \approx 128.57^o \\\\[-0.35em] ~\dotfill[/tex]
[tex]\underset{in~degrees}{\textit{sum of all exterior angles}}\\\\ n\beta = 360 ~~ \begin{cases} n=\stackrel{number~of}{sides}\\ \beta = \stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ n=7 \end{cases}\implies 7\beta=360 \\\\\\ \beta=\cfrac{360}{7}\implies \beta=51\frac{3}{7}\implies \beta\approx 51.43^o[/tex]
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