SOLUTION: the exterior of a regular polygon is 2/3 of its interior angle ,how many sides are their in the polygon.

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Question 615055: the exterior of a regular polygon is 2/3 of its interior angle ,how many sides are their in the polygon.
Found 2 solutions by Alan3354, stanbon:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Int + (2/3)*Int = 180
Int = 108
Ext = 72
n = 360/72 = 5 sides

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
the exterior of a regular polygon is 2/3 of its interior angle ,how many sides are their in the polygon.
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the interior and corresponding exterior angl are supplementary
ext = (2/3)interior
ext + int = 180
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Substitute for ext and solve for int.
(2/3)int + int = 180
(5/3)int = 180
int = (3/5)180
int = 108
ext = 72
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sum of the exterior angles = 360 degrees
# of ext = 360/72 = 5
# of sides = 5
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Cheers,
Stan H.
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