To determine the sum of the measures of the exterior angles of any convex polygon, follow this geometric property:
The sum of the measures of the exterior angles of any convex polygon, regardless of the number of sides, is always the same. Here’s why:
1. An exterior angle of a polygon is formed by extending one side of the polygon at one vertex.
2. Each exterior angle has a corresponding interior angle, and these two angles together form a linear pair, summing up to [tex]\( 180^{\circ} \)[/tex].
3. If you go around the polygon and sum all exterior angles, you effectively make one complete rotation around the polygon, which is [tex]\( 360^{\circ} \)[/tex].
Therefore, the sum of the exterior angles of any convex polygon is always:
[tex]\[ 360^{\circ} \][/tex]
So, the correct answer is:
C. [tex]\( 360^{\circ} \)[/tex]
