SOLUTION: Find the number of sides of a convex regular polygon who sum of the interior angles is 3 times the sum of the exterior angles.

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Question 1171727: Find the number of sides of a convex regular polygon who sum of the interior angles is 3 times the sum of the exterior angles.
Answer by ikleyn(52781) About Me  (Show Source):
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Let n be the number of sides.


The sum of all exterior angles is 360  degrees.


From the condition, the sum of all interior angles is 3*360 = 1080 degrees.


It gives you an equation


    180*(n-2) = 1080


which implies


    n - 2 = 1080/180 = 6.


Hence,  n = 6 + 2 = 8.


ANSWER.  n = 8  (octagon).

Solved.


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Notice that the assumption that the polygon is regular,  is  EXCESSIVE  and  UNNECESSARY:
I did not use it my solution.

The statement and the solution  BOTH  are valid for any convex polygon.