What is the relationship between the sum of the exterior angles and the number of sides?

The sum of the exterior angles of any polygon is always 360 degrees, regardless of the number of sides the polygon has. This is a fundamental property of polygons.

To understand this, consider that when you extend one side of a polygon, the exterior angle formed with the adjacent side is supplementary to the interior angle at that vertex. As you move around the polygon, adding each of these exterior angles together, you will complete a full rotation around the vertex. Since a full rotation corresponds to 360 degrees, the total of all the exterior angles adds up to this same amount, independent of the number of sides or the shape of the polygon.

This consistent total of 360 degrees helps in solving various problems involving polygons, including those related to their geometry and angular properties.