A regular octagon has rotational symmetries that correspond to multiples of \( \frac{360^\circ}{8} = 45^\circ \). To find degrees of rotation that turn the octagon onto itself and are within the specified range (greater than 0 and less than 120 degrees), we can consider the multiples of 45 degrees.
The possible rotations of the octagon are:
- \( 45^\circ \)
- \( 90^\circ \)
- \( 135^\circ \) (which is greater than 120 degrees and therefore not valid)
- \( 180^\circ \) (also not valid since it's greater than 120 degrees)
From this list, the two valid degrees of rotation that turn a regular octagon onto itself while meeting the condition of being greater than 0 and less than 120 degrees are:
- 45 degrees
- 90 degrees
Thus, the two degrees of rotation are \( 45^\circ \) and \( 90^\circ \).
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