A regular hexagon has 6 sides and is symmetrical. When you rotate a regular hexagon about its center, it can map onto itself at every \(60^\circ\) increment (which corresponds to \(360^\circ / 6 = 60^\circ\)).
This means the hexagon can be rotated by any multiple of \(60^\circ\) to still look the same. So, the possible rotations that bring the hexagon back onto itself are:
- \(0^\circ\) (no rotation)
- \(60^\circ\)
- \(120^\circ\)
- \(180^\circ\)
- \(240^\circ\)
- \(300^\circ\)
After making a full \(360^\circ\) rotation, it is back to its original position. Thus, valid multiples of degrees for turns onto itself include any multiple of \(60^\circ\), such as \(0^\circ\), \(60^\circ\), \(120^\circ\), \(180^\circ\), \(240^\circ\), \(300^\circ\), and additionally any \(k \cdot 60^\circ\) where \(k\) is an integer.
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