Question

what is the sum of the exterior angle measures, one at each vertex, of a convex decagon?

Explanation:

Step1: Recall the exterior angle sum theorem

For any convex polygon, the sum of the exterior angle measures, one at each vertex, is always \( 360^\circ \), regardless of the number of sides.

Step2: Apply the theorem to a decagon

A decagon is a convex polygon (as given in the problem), so we use the exterior angle sum theorem. The number of sides (10 for a decagon) does not affect the sum of the exterior angles for a convex polygon. So the sum of the exterior angle measures of a convex decagon is \( 360^\circ \).

Answer:

\( 360^\circ \)