[tex]\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[/tex]
How many sides does it have is 36 sides
The regular polygon of n sides is:
a=(n-2)×180/2
Solve for n
160=(n-2)×180/n
Multiply both sides by n
170n=(n-2)×180
Simplify
170n=180n-360
Subtract from both sides
0=10n-360
Divide both sides by 10
n=360/10
n=36
Inconclusion How many sides does it have is 36 sides.
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