Question

what is the sum of the measures of the exterior angles of a nonagon in degrees?

Explanation:

Step1: Recall the exterior angle sum theorem

The exterior angle sum theorem states that for any convex polygon, the sum of the measures of the exterior angles, one at each vertex, is always \(360^\circ\), regardless of the number of sides the polygon has.

Step2: Apply the theorem to a nonagon

A nonagon is a nine - sided polygon. Since the exterior angle sum theorem applies to all convex polygons (and a nonagon is a convex polygon, or even if it is not convex, the sum of exterior angles taken one at each vertex is still \(360^\circ\)), the sum of the exterior angles of a nonagon is \(360^\circ\).

Answer:

\(360\)