Question

A regular polygon has 10 sides. what is the measurement of each interior angle?

Answer 1

`\bf \textit{sum of all interior angles in a regular polygon}\\\\n\theta =180(n-2)~~\begin{cases}n=\textit{number of sides}\\\theta =interior~angle\\\qquad in~degrees\\[-0.5em]\hrulefill\\n=10\end{cases}\implies 10\theta =180(10-2)\\\\\\10\theta =180(8)\implies 10\theta =1440\implies \theta =\cfrac{1440}{10}\implies \blacktriangleright \theta =144 \blacktriangleleft`