Question

1. what is the sum of the measures of the exterior angles of a nonagon?

Explanation:

Step1: Recall the exterior angle sum theorem

For any convex polygon, the sum of the exterior angles, one at each vertex, is always \(360^\circ\). A nonagon is a polygon with 9 sides, and it is a convex polygon (assuming it is a regular or convex nonagon, but the exterior angle sum holds for any convex polygon regardless of the number of sides).

Step2: Apply the theorem to the nonagon

Since the exterior angle sum of any convex polygon is \(360^\circ\), the sum of the measures of the exterior angles of a nonagon is also \(360^\circ\).

Answer:

The sum of the measures of the exterior angles of a nonagon is \(\boldsymbol{360^\circ}\).