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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