Final answer:
A regular nonagon has nine points of rotational symmetry, and by dividing a full circle (360 degrees) by the number of symmetry points, it is determined that the nonagon has rotational symmetry at every 40 degrees.
Step-by-step explanation:
Rotational Symmetry of a Regular Nonagon
To determine the degree of rotational symmetry for a regular nonagon, one must know that a regular nonagon has nine equal sides and nine equal angles. Rotational symmetry of an object means that the object looks the same after a certain amount of rotation. A key property of regular polygons is that they have as many axes of rotational symmetry as they have sides. Therefore, a regular nonagon would have nine points of rotational symmetry. Rotational symmetry can be calculated by dividing the full circle, 360 degrees, by the number of symmetry points the shape has.
For a regular nonagon:
360 degrees / 9 = 40 degrees
Therefore, a regular nonagon has rotational symmetry at every 40 degrees. This means that if you rotate a nonagon by 40 degrees about its center, it would appear exactly as it did before rotation.
If we apply this principle to the question, we find that the answer is 40 degrees, which corresponds to option c.