Question

What is the smallest degree measure for a regular nonagon to rotate onto itself?(1 point)
Responses

80°
80 degrees

30°
30 degrees

40°
40 degrees

60°
60 degrees

pick the wrongest answer

Answer 1

A regular nonagon has 9 sides. The smallest degree measure for a regular polygon to rotate onto itself is given by the formula:

\[
\text{Angle of rotation} = \frac{360^\circ}{n}
\]

where \( n \) is the number of sides.

For a nonagon (n = 9):

\[
\text{Angle of rotation} = \frac{360^\circ}{9} = 40^\circ
\]

Thus, the smallest degree measure for a regular nonagon to rotate onto itself is 40°.

Now, to pick the "wrongest" answer from the choices:

- 80°
- 30°
- 40° (correct answer)
- 60°

The numbers 80°, 30°, and 60° do not correspond to the correct rotational symmetry of the nonagon. Among these, 80° is the largest and is further from the correct answer of 40°, making it the "wrongest" answer.

So, the answer is:

**80°**