SOLUTION: The exterior angle of a regular polygon is one-third of its interior angle. How many sides has the polygon

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Question 1037922: The exterior angle of a regular polygon is one-third of its interior angle. How many sides has the polygon

Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Sum of the interior and exterior angle at the one vertex is 180 degrees for a straight angle.

The two angles are v and 3v.
v%2B3v=180
4v=180
v=180%2F4
v=2%2A3%2A3%2A2%2A5%2F%282%2A2%29
highlight%28v=45%29--------the exterior angle. The interior angle is 135 degrees.

A route of thinking: Starting with a triangle, regular polygon has 180 degrees, sum of the interior angles. Four sides is added another 180 degrees. 5 sides, another 180 degrees.
--
You can build a chart of this. 
n        Interior Degrees     Degrees at a vertex
3            180                 60
4            360                 90
5            540                108
6            720                120
7            900                128.57
8           1080                135

There it is. Eight sides regular polygon.

Answer by MathTherapy(10551) About Me  (Show Source):
You can put this solution on YOUR website!

The exterior angle of a regular polygon is one-third of its interior angle. How many sides has the polygon 
Let one of the exterior angles be E

Then one of the interior angles is: 3E

Since the exterior and interior angles are supplementary, we get: E + 3E = 180

4E = 180

E, or one of the EXTERIOR angles = 180%2F4, or 45o

Since the exterior angles of any polygon sum to 360o, we can say that the number of sides of the polygon = 360%2F45, or highlight_green%288%29, thus making it an OCTAGON.