How many angle rotations between 1 and 360 degrees about the center point will carry a regular octagon onto itself

 The number of angle rotations is 7.

Step-by-step explanation:  To find the angle of rotation of a regular polygon, we have to divide the total angle about origin, i.e., 360° by the number of equal sides of the polygon.

Let ABCDEFGH be a regular octagon with centre "O".

We are to find the angle of rotation of regular octagon ABCDEFGH.

Now, number of sides in the octagon = 8.

Therefore, the angle of rotation which maps the octagon onto itself is given by

Thus, the angles of rotation lying between 1 ° and 360° are

45°, 2×45°, 3×45°, 4×45°, 5×45°, 6×45° and 7×45°

= 45°, 90°, 135°, 180°, 225°, 270° and 315°.

Thus, the total number of angle rotations is 7.

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step-by-step explanation: