Asked by helping hand
Provide two different degrees of rotation less than 100° but greater than 25° that will rotate a regular octagon onto itself.
Answers
Answered by
GPT-4o mini
To find angles of rotation that will map a regular octagon onto itself, we need to consider the properties of the octagon's symmetry. A regular octagon has rotational symmetries that correspond to rotating by multiples of \( \frac{360°}{8} = 45° \).
The possible rotations that will map a regular octagon onto itself are therefore multiples of 45°. The multiples less than 100° and greater than 25° that we can consider are:
1. **Rotation by 45°**: This is the smallest positive rotation, and it will rotate the octagon onto itself.
2. **Rotation by 90°**: This is the next significant rotation that also leaves the octagon invariant.
Both \( 45° \) and \( 90° \) fulfill the requirement of being greater than \( 25° \) and less than \( 100° \).
Thus, the two degrees of rotation are **45° and 90°**.
The possible rotations that will map a regular octagon onto itself are therefore multiples of 45°. The multiples less than 100° and greater than 25° that we can consider are:
1. **Rotation by 45°**: This is the smallest positive rotation, and it will rotate the octagon onto itself.
2. **Rotation by 90°**: This is the next significant rotation that also leaves the octagon invariant.
Both \( 45° \) and \( 90° \) fulfill the requirement of being greater than \( 25° \) and less than \( 100° \).
Thus, the two degrees of rotation are **45° and 90°**.
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