To find the smallest degree measure for a regular nonagon (a polygon with 9 sides) to rotate on itself, we need to determine the angle of rotation that maps the nonagon onto itself.
The interior angle for any regular polygon can be calculated using the formula: \[ \text{Interior angle} = \frac{(n-2) \times 180^\circ}{n} \]
However, for the purpose of finding the rotational symmetry, we focus on the full rotational angle, which is \(360^\circ\), and divide that by the number of sides in the polygon.
For a regular nonagon (where \(n = 9\)): \[ \text{Rotational symmetry angle} = \frac{360^\circ}{n} = \frac{360^\circ}{9} = 40^\circ \]
This means that rotating the nonagon by \(40^\circ\) results in the nonagon mapping onto itself. Therefore, the smallest degree measure for a regular nonagon to rotate on itself is:
\[ \boxed{40} \]
1 answer