A regular hexagon has rotational symmetry and can rotate onto itself at specific angles corresponding to its internal symmetry. The full rotation of a hexagon is 360 degrees, and it can be turned onto itself in multiples of 360 degrees divided by the number of sides.
For a regular hexagon (which has 6 sides), the possible angles of rotation that allow it to coincide with its original position are given by:
\[ \text{Angles} = \frac{360^\circ}{6} \times n \quad \text{where } n = 0, 1, 2, ..., 5 \]
This results in the following angles:
- \( n = 0 \): \( 0^\circ \)
- \( n = 1 \): \( 60^\circ \)
- \( n = 2 \): \( 120^\circ \)
- \( n = 3 \): \( 180^\circ \)
- \( n = 4 \): \( 240^\circ \)
- \( n = 5 \): \( 300^\circ \)
Thus, the angles of rotation that allow the regular hexagon to turn onto itself are:
- 60
- 120
- 180
- 240
- 300
Therefore, the correct responses are:
- 60
- 120
- 180
- 240
- 300
1 answer