Answer:
The sum of the exterior angles of any polygon always equals 360 degrees. Let's prove this for a polygon with n sides:
1. Start with a polygon with n sides.
2. Extend each side of the polygon to form its corresponding exterior angle.
3. Each interior angle of the polygon pairs with an exterior angle to form a straight line (180 degrees).
4. Since there are n interior angles in the polygon, there are also n exterior angles.
5. The sum of all the interior angles of a polygon with n sides is given by the formula: (n - 2) * 180 degrees. This is a well-known result in geometry.
6. Therefore, the sum of all the exterior angles must be equal to 360 degrees because each interior-exterior angle pair forms a straight line (180 degrees), and there are n such pairs.
So, in general, for any polygon with n sides, the sum of its exterior angles is always 360 degrees.