To determine the sum of the exterior angle measures of any polygon, it is important to know a fundamental property of polygons: the sum of the exterior angles of any polygon is always the same.
For any polygon, regardless of the number of sides, the sum of the exterior angles is always:
[tex]\[ 360 \text{ degrees} \][/tex]
This applies whether the polygon is a triangle, quadrilateral, pentagon, hexagon, or any other polygon, including a nonagon (nine-sided polygon).
Given that the sum of the exterior angle measures of any polygon is [tex]\( 360 \)[/tex] degrees, we can immediately conclude that the sum of the exterior angle measures for a regular nonagon (a polygon with 9 equal sides) is:
[tex]\[ 360 \text{ degrees} \][/tex]
Therefore, the correct answer is:
A. 360
