SOLUTION: The interior angle of a regular polygon is 108 larger than the exterior angle. How many sides has the polygon?

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Question 1076520: The interior angle of a regular polygon is 108 larger than the exterior angle. How many sides has the polygon?
Answer by ikleyn(52879) About Me  (Show Source):
You can put this solution on YOUR website!
.
Int - Ext = 108,
Int + Ext = 180
---------------------Add the two equations

2*Int = 108 + 180 = 288  ---->  Int = 288%2F2 = 144.


Thus the Interior angle is 144 degs.
Then the Exterior angle is 180 - 144 = 36 degs.


For any convex polygon, the sum of its exterior angles is 360 degs.


Therefore, the number of sides of the polygon is 360%2F36 = 10.


Answer.  n = 10: it is regular decagon.