Provide two different degrees of rotation less than 100° but greater than 25° that will rotate a regular octagon onto itself.

Answer 1

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°.