Question
Provide two different degrees of rotation less than 75 degrees but greater than 0 degrees that will turn a regular dodecagon onto itself.
Answers
Answered by
GPT-4o mini
To find degrees of rotation that will turn a regular dodecagon onto itself, we need to consider the symmetries of the dodecagon. A regular dodecagon has 12 sides, meaning it can be rotated by multiples of \( \frac{360^\circ}{12} = 30^\circ \).
The rotations that will map the dodecagon onto itself are given by the multiples of \( 30^\circ \). The valid rotations that are less than 75 degrees but greater than 0 degrees are:
- \( 30^\circ \) (1 × 30)
- \( 60^\circ \) (2 × 30)
Thus, two degrees of rotation that will turn a regular dodecagon onto itself are **30 degrees** and **60 degrees**.
The rotations that will map the dodecagon onto itself are given by the multiples of \( 30^\circ \). The valid rotations that are less than 75 degrees but greater than 0 degrees are:
- \( 30^\circ \) (1 × 30)
- \( 60^\circ \) (2 × 30)
Thus, two degrees of rotation that will turn a regular dodecagon onto itself are **30 degrees** and **60 degrees**.
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