SOLUTION: the exterior angle of a regular polygon is equal to One-third of the interior angle. calculate the number of sides of the polygon and give its name?
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Question 1091691: the exterior angle of a regular polygon is equal to One-third of the interior angle. calculate the number of sides of the polygon and give its name? Answer by htmentor(1343) (Show Source):
You can put this solution on YOUR website! The sum of the interior and exterior angles = 180
Let x = the interior angle
Then x + x/3 = 180 -> x = 3/4*180 = 135
Also the interior angle of a regular polygon can be determined by:
x = 180((n-2)/n) = 135
Solve for n:
135n = 180n - 360 -> n = 8
Thus the polygon is an octagon
