Provide two different degrees of rotation less than 120 degrees but greater than 0 that will turn a regular octagon onto itself.

Answer 1

To find the degrees of rotation that will turn a regular octagon onto itself, we need to consider the properties of a regular octagon. An octagon has eight sides, and it can be rotated at angles that are multiples of \( \frac{360^\circ}{8} = 45^\circ \).

The angles of rotation that will turn the octagon onto itself are therefore multiples of \( 45^\circ \): \( 0^\circ, 45^\circ, 90^\circ, 135^\circ, 180^\circ, 225^\circ, 270^\circ, 315^\circ \).

Since we need to find two different degrees of rotation that are greater than \( 0^\circ \) and less than \( 120^\circ \), the suitable angles from this list are:

1. \( 45^\circ \)
2. \( 90^\circ \)

Thus, the two different degrees of rotation are \( 45^\circ \) and \( 90^\circ \).

Answer 2

A circle measures 360 degrees. If this circle were marked with numbers like a clock, every number would represent 30 degrees farther from 0 and closer to 360 degrees.
If an angle marker typically found at 10:00 were to rotate to the place normally marked for 5:00, what is the degree measure of the angle formed moving counterclockwise?