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(52788)   (Show Source): You can put this solution on YOUR website!
.
Let  x  be the measure of the interior angle in degrees.
then the exterior angle is    and their sum is

+ = 180°.

Hence,  x = = 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.



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