Math. please explain well?

Question

For a polygon with the given number of sides, find the sum of the measures of the exterior angles, one angle at each vertex.
What is the answer if I was working with 40 sides

Answer 1

360 degrees
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Reason: Exterior angle sum theorem for any polygon.

Answer 2

How ever many sides a polygon has the exterior angles will always add up to 360 degrees.

Think about it like this. The more sides a polygon has the smaller the angles get, so the fact that there are more angles to add up cancels out.

You can also test it out by first drawing a polygon. Then take a pen and place it on one of the sides. Keep turning the pen onto each side of the polygon and eventually it will end up the same way up as before having made one full 360 degree rotation.

Hope this helped.

Answer 3

a very interesting problem.
I first consider a square and I get 360 degrees. Then I look at a circle as the limit of regular polygon as the number of sides approache infinity and each exterior angle approaches zero.
I am forced to the conclusion that the answer must be 360 degrees. May even be true for any closed polygon.
A quick check of an equalateral triangle gives 360 degrees.

Answer 4

The sum of the exterior angles of any polygon is 360 degrees regardless of the number of sides. So 40 sides is 360 degrees. It is 360 degrees for 1,000,000 sides.

Answer 5

There's a formula for finding the total # of degrees in any number polygon; which is:
(x-2)*180=n
x= # of sides and
n= total of degrees.
To fnd each angle, you divide by the # of sides.
Each angle = a total of 360.
You subtract this from 360 to get the outside angle.
Then you multiply by the # of angles to find your total outside degrees.

In math formula form:

(360-(x-2)*180/x)*x= sum of outside angles

or simplified to:

180*(x+2)= sum of outside angles

Your answer would be (40+2)*180 or 7,560 degrees.