prove that the sum of the exterior angles of a polygon is 360 degree.

Question

1. take examples and verify
2. anallitically proof
3. geometrically proof
4. conclusion

I want a best of all answer

Answer 1

The sum of the interior angles of a regular polygon with n sides is 180(n-2).

So, each interior angle has measure 180(n-2) / n.

Each exterior angle is the supplement to an interior angle.

So, the measure of an exterior angle is:

180 - 180(n-2) / n = [180n - 180n + 360] / n

= 360/n

Sum of exterior angles = n(360 / n) = 360.