A regular hexagon has 6 sides, and it can be rotated about its center by multiples of \( \frac{360^\circ}{6} = 60^\circ \). This means it will align with its original position after every rotation of 60 degrees.
The turns that allow the hexagon to turn onto itself (i.e., bring it back to an equivalent position) are the multiples of 60 degrees up to 360 degrees.
The valid degrees of turns that allow the regular hexagon to turn onto itself are:
- 60 degrees (1 turn)
- 120 degrees (2 turns)
- 180 degrees (3 turns)
- 240 degrees (4 turns)
- 300 degrees (5 turns)
- 360 degrees (6 turns)
Thus, the applicable responses are:
- 60
- 120
- 180
- 240
- 300
- 360
You can check those options off in your response!