SOLUTION: What is the number of sides in the polygon? The measure of an exterior angle of a regular polygon is 2x, and the measure of an interior angle is 4x.

Algebra ->  Polygons -> SOLUTION: What is the number of sides in the polygon? The measure of an exterior angle of a regular polygon is 2x, and the measure of an interior angle is 4x.       Log On


   

Question 1001860: What is the number of sides in the polygon? The measure of an exterior angle of a regular polygon is 2x, and the measure of an interior angle is 4x.
Found 2 solutions by solver91311, MathTherapy:
Answer by solver91311(24713) About Me  (Show Source):
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The measure of an exterior angle of any regular polygon is

The measure of an interior angle of any regular polygon is

Since the measure of an interior angle of the polygon under consideration is two times the measure of the exterior angle, we can say that:



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John

My calculator said it, I believe it, that settles it

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

What is the number of sides in the polygon? The measure of an exterior angle of a regular polygon is 2x, and the measure of an interior angle is 4x. 
With an exterior angle being 2x, an interior angle being 4x, and since an exterior and interior angle are supplementary (sum to 180o), we get: 

2x + 4x = 180

6x = 180

x = 180%2F6, or 30

One exterior angle = 2x, or 2(30), or 60%5Eo

Number of sides: 360%2F60, or highlight_green%286%29 (hexagon)