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..

Algebra.Com
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): 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 number of sides is n where (n-2)*180 = sum of interior angles.
--------------------------------------------------------------------
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
------------------------
since n is a whole number, n = 13 or 14
-----------------------
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
RELATED QUESTIONS

The sum of the measures of the interior angles of a polygon is between 2100 and 2400. how (answered by mangopeeler07)
If the sum of the interior angles of a polygon is 1800° where one of the interior angles... (answered by Edwin McCravy)
How many sides does a polygon have if the sum of the measures of the interior angles is... (answered by jim_thompson5910)
The sum of the measures of the interior angles of a regular polygon is 2340 degrees. How... (answered by stanbon)
the sum of the measures of the interior angles of a polygon is 540 dergees. Exactly how... (answered by Alan3354)
The sum of the measures of the interior angles of a convex polygon is 1980. How many... (answered by stanbon)
the sum of the measures of the interior angles of a convex polygon is 1980. how many... (answered by stanbon,shree840)
The sum of the measures of the interior angles of a polygon is 1620°. How many sides does (answered by KMST)
the sum of the measures of the interior angles of a regular polygon is 2340 (degrees).... (answered by Don2xmalabag)