Questions on Geometry: Polygons answered by real tutors!

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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.

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