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

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) (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.

--------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) (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 = , or 45^o
Since the exterior angles of any polygon sum to 360^o, we can say that the number of sides of the polygon = , or , thus making it an OCTAGON.
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