What is the sum of the exterior angle measures, one at each vertex, of a convex polygon with 19 sides?

The sum of the exterior angle measures of any convex polygon, regardless of the number of sides, is always 360 degrees. This is because when you walk around a polygon, making one full turn at each vertex, you complete a full circle, which is 360 degrees.<br /><br />So, for a convex polygon with 19 sides, the sum of the exterior angle measures is 360 degrees.