SOLUTION: How many sides does a regular polygon have if its interior angle measures 120 degrees?

Algebra ->  Angles -> SOLUTION: How many sides does a regular polygon have if its interior angle measures 120 degrees?      Log On


   

Question 153393: How many sides does a regular polygon have if its interior angle measures 120 degrees?
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
The measure of an interior angle of a regular polygon of n sides is given by:
A%5Bi%5D+=+%28n-2%29180%2Fn In this problem, the interior angle is 120 degrees, so...
%28n-2%29180%2Fn+=+120 Simplify and solve for n. Multiply both sides by n.
%28n-2%29180+=+120n Expand the left side.
180n-360+=+120n Subtract 120n from both sides.
60n+-+360+=+0 Now add 360 to both sides.
60n+=+360 Finally, divide both sides by 60.
n+=+6
The regular polygon has 6 sides, and this is called a hexagon.