To determine which angles of rotation would not map a regular nonagon onto itself, we need to consider the angles that would allow the nonagon to look the same after rotation.
A regular nonagon has 9 sides, and therefore can be rotated by multiples of \( \frac{360^\circ}{9} = 40^\circ \) to map it onto itself. This means any angle that is a multiple of 40 degrees is a valid angle of rotation that maps the nonagon onto itself.
The angles of rotation we were given are:
- 60°
- 120°
- 80°
- 40°
Now we can check each of these angles to see if they are multiples of 40°:
- 60°: \( 60^\circ \div 40^\circ = 1.5 \) (not a multiple)
- 120°: \( 120^\circ \div 40^\circ = 3 \) (multiple of 40)
- 80°: \( 80^\circ \div 40^\circ = 2 \) (multiple of 40)
- 40°: \( 40^\circ \div 40^\circ = 1 \) (multiple of 40)
From this analysis, the angle that does not map the regular nonagon onto itself is:
60°.