Let's solve the problem step-by-step:
1. Understanding Rotational Symmetry:
- The order of rotational symmetry of a shape is the number of times the shape maps onto itself during a 360-degree rotation. For a regular polygon, this is equal to the number of sides.
2. Determining the Order of Rotational Symmetry:
- Since we are dealing with a regular octagon, it has 8 sides.
- Therefore, the order of rotational symmetry is 8. This means the octagon maps onto itself 8 times during a full 360-degree rotation.
3. Calculating the Angle of Rotation:
- The angle of rotation for a regular polygon can be found by dividing 360 degrees by the number of sides.
- For a regular octagon, this angle is [tex]\( \frac{360^\circ}{8} \)[/tex].
4. Performing the Division:
- [tex]\( \frac{360^\circ}{8} = 45^\circ \)[/tex].
Thus, the order of rotational symmetry for a regular octagon is 8, and the angle of rotation is 45 degrees.
The correct answer is:
[tex]\[ \text{Order} = 8, \text{angle of rotation} = 45^\circ \][/tex]
