SOLUTION: find the no of sides of regular convex polygon whose angle is 40 deg?

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Question 33843: find the no of sides of regular convex polygon whose angle is 40 deg?
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
The measure of one vertex angle of a regular polygon is given by:
%28n-2%29180%2Fn where n is the number of sides of the regular polygon...and, of course, it goes without saying, that n must be an integer >2(i.e, 3, 4, 5, 6, ...).
If the measure of one vertex angle of a regular polygon is 40 degrees, then we can write:
%28n-2%29180%2Fn+=+40 Simplify and solve for n.
%28180n-360%29%2Fn+=+40 Multiply both sides by n.
180n+-+360+=+40n Add 360 to both sides.
180n+=+360%2B40n Subtract 40n from both sides.
140n+=+360 Divide both sides by 140.
n+=+2.57 This is not possible since a regular polygon must have an integral numer of sides.
Conclusion:
There is no regular polygon whose vertex angle is 40 degrees.