Geometry

[goodyhi11]

I have a geometry problem that need to be solved. Any one volunteer?

 

Problems: The measure of each exterior angle of an equianglar polygon is half the measure of each interior angle of the polygon. What is the name of the polygon?

 

Thanks

[ed84c]

Hexagon

[goodyhi11]

hey that's what I thought too, but that's not the answer, the answer is equlateral, and I have no clue how the answer is that.

[ed84c]

parallelagram

[Sayonara]

Isn't it parallelogram?

[goodyhi11]

yes "sayonara3", you are right, but how did you figure it out though?

[swansont]

A parallelogram doesn't have a fixed angle, nor are all the angles necessarily the same, so it can't be the answer.

 

The sum of the angles is 180. If the exterior is half the interior, then it's 60 exterior and 120 interior. Hexagon.

 

Are you sure you copied the question correctly? If you reverse the relationship then you get 60 degrees for the interior angle, which would be an equilateral triangle.

[goodyhi11]

A parallelogram doesn't have a fixed angle, nor are all the angles necessarily the same, so it can't be the answer.

 

The sum of the angles is 180. If the exterior is half the interior, then it's 60 exterior and 120 interior. Hexagon.

 

Are you sure you copied the question correctly? If you reverse the relationship then you get 60 degrees for the interior angle, which would be an equilateral triangle.

 

You are right, it is a hexagon. Can you please expain your steps again?

[Sayonara]

yes "sayonara3", you are right, but how did you figure it out though?

I wasn't giving that as an answer - it was pedantry at work.

[swansont]

You are right, it is a hexagon. Can you please expain your steps again?

 

The relations that are important are that (exterior angle) * (# of sides) = 360, and the sum of the two angles is 180. Since you know the relation between the two angles, you can solve for the interior angle, and thus, the number of sides.