To determine the smallest degree measure for a regular nonagon to rotate onto itself, we first need to understand the properties of a regular nonagon.
A regular nonagon has 9 sides, and it can rotate in incremental angles based on the total degrees in a circle (360 degrees) divided by the number of sides (9). Thus, the angle of rotation for the nonagon is calculated as follows:
\[ \text{Angle of rotation} = \frac{360^\circ}{9} = 40^\circ \]
This means that rotating the nonagon by 40 degrees will map it onto itself. Therefore, for the nonagon, the smallest degree measure for it to rotate onto itself is:
\[ \boxed{40} \]
Thus, the answer is (a) 40 degrees.
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