SOLUTION: why is it not possible yo draw a regular polygon with 100 degree interior angles?

Question 998540: why is it not possible yo draw a regular polygon with 100 degree interior angles?

Answer by ikleyn(52800) (Show Source): You can put this solution on YOUR website!
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Answer. It is not possible to draw a regular polygon with 100 degree interior angles because such a polygon does not exist.

Proof

Let us assume that it does exist.

Then

100*n = 180*(n-2) (it is the sum of interior angles in the left and in the right side).

Now try to solve this equation for integer n.

100*n = 180*n - 360,

80n = 360,

but 360 is not multiple of 80. Contradiction.

The proof is completed.

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