Provide two different examples of the rotation less than 75 but greater than 0 that will turn a regular dodecagon onto itself

1 answer

Example 1:
- Rotation of 30 degrees: This will turn the dodecagon by an angle of 30 degrees in a counterclockwise direction. After a full rotation by 360 degrees, the dodecagon will align with itself since 360 divided by 30 equals 12. Therefore, this rotation will preserve the regular dodecagon's symmetry and position.

Example 2:
- Rotation of 60 degrees: This will turn the dodecagon by an angle of 60 degrees in a counterclockwise direction. Similar to the previous example, after a full rotation by 360 degrees, the dodecagon will align with itself since 360 divided by 60 equals 6. Thus, this rotation also preserves the regular dodecagon's symmetry and position.