Question

What is the smallest degree measure for a regular nonagon to rotate on itself?
A. 40
B. 30
C. 80
D. 60

Answer 1

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:

\[
\boxed{40}
\]