SOLUTION: in a regular polygon each interior angle isthrice of exterior angle .the number of side poly gon

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Question 997712: in a regular polygon each interior angle isthrice of exterior angle .the number of side poly gon
Answer by ikleyn(52787) About Me  (Show Source):
You can put this solution on YOUR website!
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Let  x  be the measure of the interior angle in degrees.
then the exterior angle is  x%2F3  and their sum is

x+ + x%2F3 = 180°.

Hence,  x = %283%2A180%29%2F4 = 135°.

The sum of interior angles is n*135°.
From the other side, it is (n-2)*180.

So, we have an equation

(n-2)*180 = n*135.

Divide both sides by 45. You will get

(n-2)*4 = n*3, or

4n - 8 = 3n,

4n - 3n = 8,

n = 8.

Our polygon is octagon.