Answer: 360°.
Explanation.
The sum of the measures of the exterior angles of any simple polygon is 360°. That is true for triangles, rectangles, pentagons, hexagons, a so on, any polygon including, of course, the nonagon.
You can verify this if you draw the nonagon with its 9 exterior angles. You can realize that you may translate every angle to one common vertex and that the sum of all angles is equal to a complete turn around the vertex. Of course, you know that a complete turn is an agle of 360°.