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.

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) (Show Source): You can put this solution on YOUR website!

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:

Solve for

John

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

Answer by MathTherapy(10552) (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 180^o), we get:
2x + 4x = 180
6x = 180
x = , or 30
One exterior angle = 2x, or 2(30), or
Number of sides: , or (hexagon)
RELATED QUESTIONS
What is the number of degrees in the measure of each exterior angle of a regular polygon... (answered by Alan3354)
the measure of one exterior angle of a regular polygon is 175degrees find the number of... (answered by Mathtut)
In a certain regular polygon, the measure of an interior angle is equal to the measure of (answered by richard1234)
What is the measure of an exterior angle in a regular polygon with 44 sides? please... (answered by MathLover1)
what is the measure of each exterior angle of a regular polygon with 100... (answered by ewatrrr)
if an exterior angle of a regular polygon is 24 how many sides does the polygon have and... (answered by Alan3354)
If the measure of an exterior angle of a regular polygon is 15, how many sides does the... (answered by Alan3354)
if the measure of an exterior angle of a regular polygon is 36, how many sides does the... (answered by Alan3354)
The measure of an exterior angle of a regular polygon is 'x'. How many sides does the... (answered by Boreal)