Question

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

Explanation:

Step1: Recall the exterior angle theorem for polygons

For any polygon, the sum of the exterior angles (one at each vertex) is always \(360^\circ\) when considering convex polygons. A triangle is a convex polygon (in the standard case we consider for basic geometry).

Step2: Apply the theorem to a triangle

Since a triangle is a polygon with three sides, using the general result for the sum of exterior angles of a polygon, the sum of the exterior angle measures (one at each vertex) of a triangle is \(360^\circ\).

Answer:

\(360^\circ\)