To determine the sum of the measures of the exterior angles of a convex hexagon, recall an important property of polygons. The sum of the exterior angles of any convex polygon, regardless of the number of sides, is always [tex]\(360^\circ\)[/tex]. This is because the exterior angles, one at each vertex, effectively form a full circle around the polygon.
Given that a hexagon has 6 sides, let's analyze it step by step:
1. Understanding exterior angles: An exterior angle of a polygon is formed by extending one of its sides. At each vertex of the hexagon, you can form an exterior angle.
2. Sum of exterior angles for any polygon: For any convex polygon, the sum of the exterior angles is always [tex]\(360^\circ\)[/tex]. This is true irrespective of the number of sides.
3. Application to a hexagon: Since a hexagon is a type of convex polygon, the sum of its exterior angles will also be [tex]\(360^\circ\)[/tex].
Thus, the sum of the measures of the exterior angles of a convex hexagon is [tex]\(\boxed{360^\circ}\)[/tex].
