Question

what is the smallest degree measure for a regular nonagon to rotate onto itself? (1 point)
○ 40°
○ 80°
○ 30°
○ 60°

Explanation:

Step1: Recall rotation symmetry formula

For a regular \( n \)-sided polygon, the smallest angle of rotation (the angle by which it can be rotated to map onto itself) is given by the formula \( \frac{360^{\circ}}{n} \), where \( n \) is the number of sides.

Step2: Identify \( n \) for a nonagon

A nonagon has 9 sides, so \( n = 9 \).

Step3: Calculate the rotation angle

Substitute \( n = 9 \) into the formula: \( \frac{360^{\circ}}{9}= 40^{\circ} \).

Answer:

\( 40^{\circ} \) (corresponding to the option "40°")