SOLUTION: the sum of the interior angles of a polygon is three times the sum of its exterior angles . Determine the number of sides of the polygon

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Question 1040556: the sum of the interior angles of a polygon is three times the sum of its exterior angles . Determine the number of sides of the polygon
Answer by ikleyn(52781) About Me  (Show Source):
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the sum of the interior angles of a polygon is three times the sum of its exterior angles . Determine the number of sides of the polygon
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(n-2)*180 = 3*360  --->   (Everybody knows about the left side. It is the sum of internal angles of any n-sided polygon.
                           Many know about the number 360 in the right side. 360° is the sum of the external angles of any n-sided polygon.)

n- 2 = %283%2A360%29%2F180 = 3*2 = 6  --->

n = 6 + 2 = 8.

Check.  (8-2)*180 = 6*180.   6*180 in the left = 3*360 in the right.   Yes!!!

Answer.  n = 8.   ( Octagon ! )