A regular nonagon has 9 sides. To find the smallest degree measure that a regular nonagon can rotate onto itself, we can calculate the angle of rotation for one of its vertices.
The formula to find the angle of rotation for a regular polygon is:
\[ \text{Angle of rotation} = \frac{360°}{n} \]
where \( n \) is the number of sides.
For a nonagon (\( n = 9 \)):
\[ \text{Angle of rotation} = \frac{360°}{9} = 40° \]
Thus, the smallest degree measure for a regular nonagon to rotate onto itself is:
40°
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