The sum of the interior angles of a polygon with n sides is 1980°. Find n.

Xavier Dury asked Aug 17, 2023

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Xavier Dury asked Aug 17, 2023

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21 votes

We can relate the sum of the interior angles of a polygon S with its number of sides n as:

$S=(n-2)\cdot180$

Then, if S=1980 degrees, we can find n as:

$\begin{gathered} 1980=(n-2)\cdot180 \\ n-2=(1980)/(180) \\ n-2=11 \\ n=11+2 \\ n=13 \end{gathered}$

Answer: the polygon has 13 sides (n=13)

Fez answered Aug 24, 2023

by Fez

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