Mathematics, 06.12.2019 01:31 alexandria3498
An interior angle of a regular polygon measures 170 degrees. how many sides does it have?
Answers: 1
![\bf \textit{sum of all interior angles in a polygon}\\\\ n\theta =180(n-2)~~ \begin{cases} n= \stackrel{number~of}{sides}\\ \theta =\stackrel{angle~in}{degrees}\\[-0.5em] \hrulefill\\ \theta =170 \end{cases}\implies n170=180(n-2) \\\\\\ 170n=180n-360\implies 170n+360=180n\implies 360=10n \\\\\\ \cfrac{360}{10}=n\implies 36=n](/tpl/images/0405/5564/2fce2.png)
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