A regular hexagon can be turned onto itself when the angle of rotation is a multiple of the angles between its vertices. The angle between adjacent vertices of a regular hexagon is:
\[ \frac{360^\circ}{6} = 60^\circ. \]
Thus, the hexagon will turn onto itself for any multiple of this angle:
- 0° (no turn)
- 60° (1 vertex turn)
- 120° (2 vertex turns)
- 180° (3 vertex turns)
- 240° (4 vertex turns)
- 300° (5 vertex turns)
These angles can be represented as \( n \times 60^\circ \), where \( n \) is an integer from 0 to 5.
From your list, the degrees of turns that allow the regular hexagon to turn onto itself are:
- 60
- 120
- 180
- 240
- 300
The other angles (30, 90, 150, 210, 270, and 330) do not align with the symmetry of the hexagon and thus do not rotate it onto itself.
So, the correct answers are:
- 60
- 120
- 180
- 240
- 300