A regular nonagon has 9 sides. To find the smallest degree measure for it to rotate onto itself, we can calculate the angle of rotation that corresponds to one vertex moving to the position of the next vertex.
The formula for calculating the angle of rotation for a regular polygon is:
\[ \text{Angle} = \frac{360^\circ}{n} \]
where \( n \) is the number of sides.
For a nonagon, \( n = 9 \):
\[ \text{Angle} = \frac{360^\circ}{9} = 40^\circ \]
Therefore, the smallest degree measure for a regular nonagon to rotate onto itself is 40 degrees.
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