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Given the sum of the interior angle measures, find the number of sides.

Given the sum of the interior angle measures, find the number of sides.-example-1
User Skalb
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Recall that the sum of the interior angles of a convex polygon with n sides is:


(n-2)*180^(\circ).

Therefore:

12) If the sum of the interior angles of a convex polygon is 3240 degrees, then we can set the following equation:


(n-2)*180^{}=3240.

Dividing the above equation by 180 we get:


\begin{gathered} ((n-2)*180)/(180)=(3240)/(180), \\ n-2=18. \end{gathered}

Adding 2 to the above equation we get:


\begin{gathered} n-2+2=18+2, \\ n=20. \end{gathered}

13) If the sum of the interior angles of a convex polygon is 6660 degrees, then we can set the following equation:


(n-2)*180=6660.

Dividing the above equation by 180 we get:


\begin{gathered} ((n-2)*180)/(180)=(6660)/(180), \\ n-2=37. \end{gathered}

Adding 2 to the above equation we get:


\begin{gathered} n-2+2=37+2, \\ n=39. \end{gathered}

Answer:

12) 20.

13) 39.

User Kevin Rave
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