SOLUTION: If the sum of the interior angles in a regular polygon is 3600o , then what is the value of each interior angle? How many sides does it have?

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Question 1173719: If the sum of the interior angles in a regular polygon is 3600o
, then what is the value of each interior
angle? How many sides does it have?
Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The sum of the measures of a polygon is 180(n-2), where n is the number of sides.

180%28n-2%29+=+3600
n-2+=+20
n+=+22

The polygon has 22 sides; the measure of each interior angle is 3600/22 degrees.

Answer by ikleyn(52795) About Me  (Show Source):
You can put this solution on YOUR website!
.

For any convex polygon with n sides, the sum of interior angles is  180*(n-2)  degrees.


Since in your case this sum is  3600°, it gives you this equation


    180*(n-2) = 3600.


Divide it by 180 (both sides) to get


    n-2 = 3600/180 = 20;  

     n  = 20 + 2 = 22.


So, your polygon has 22 sides.    ANSWER

Solved.