Answer: 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
[tex]\dfrac{360^\circ}{8}=45^\circ.[/tex]
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.
