Explain how to calculate the measures of the angles of rotational symmetry for a regular hexagon.

Answer 1

To calculate the measures of the angles of rotational symmetry for a regular hexagon, follow these steps:

1. Recall that a regular hexagon has six equal sides and six equal angles.
2. Each angle of a regular hexagon measures 120 degrees (360 degrees divided by 6).
3. Now, consider the concept of rotational symmetry. When a regular hexagon is rotated around its center point, it will appear unchanged after every 60 degrees of rotation (360 degrees divided by the number of sides, which is 6).
4. To find the measures of the angles of rotational symmetry, you need to determine the number of times the hexagon can be rotated by 60 degrees to return to its original position.
5. Since a hexagon has rotational symmetry at every 60 degrees, it can be rotated a total of 6 times (360 degrees divided by 60 degrees).
6. Therefore, the measures of the angles of rotational symmetry for a regular hexagon are 60 degrees, 120 degrees, 180 degrees, 240 degrees, 300 degrees, and 360 degrees.

In summary, a regular hexagon has angles of rotational symmetry at every 60 degrees, totaling 6 angles of symmetry: 60°, 120°, 180°, 240°, 300°, and 360°.