A regular nonagon has 9 sides. To find the smallest degree measure for a regular nonagon to rotate onto itself, we can use the formula for the angle of rotation that maps the polygon onto itself, which is given by:
\[ \text{Rotation Angle} = \frac{360°}{n} \]
where \( n \) is the number of sides of the polygon. For a nonagon, \( n = 9 \):
\[ \text{Rotation Angle} = \frac{360°}{9} = 40° \]
Therefore, the smallest degree measure for a regular nonagon to rotate onto itself is 40°.
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