SOLUTION: the sum of the measures of the interior angles of a polygon is between 2100 and 2400. how many sides does the polygon have? thanks..

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Question 135203: the sum of the measures of the interior angles of a polygon is between 2100 and 2400. how many sides does the polygon have? thanks..

Found 2 solutions by stanbon, Edwin McCravy:
Answer by stanbon(75887) (Show Source):
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the sum of the measures of the interior angles of a polygon is between 2100 and 2400. how many sides does the polygon have? thanks..
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The number of sides is n where (n-2)*180 = sum of interior angles.
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INEQUALITY:
2100 <= (n-1)*180 <= 2400
35/3 <= n-1 <= 40/3
Add one along the line to get:
38/3 <= n <= 43/3
12 2/3 <= n <= 14 1/3
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since n is a whole number, n = 13 or 14
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Cheers,
Stan H.

Answer by Edwin McCravy(20060) (Show Source):
You can put this solution on YOUR website!
the sum of the measures of the interior angles of a polygon is between 2100 and 2400. how many sides does the polygon have? thanks.

The expression for the sum of the interior angles of an -sided polygon is: � Divide all three sides by Add to all three sides: Divide all three sides by must be an integer and the only two integers between and are and . So the polygon could either 1. have sides, with the sum of the interior angles being � � � � OR 2. have sides, with the sum of the interior angles being � � � � So there are two solutions. The number of sides is or . Edwin