To determine the order of rotational symmetry and the angle of rotation for a regular octagon, we need to follow a few logical steps:
1. Identify the Order of Rotational Symmetry:
- The order of rotational symmetry of any regular polygon (a polygon with all sides and angles equal) is equal to the number of sides it has.
- Since we are dealing with a regular octagon, which has 8 sides, the order of rotational symmetry is [tex]\(8\)[/tex].
2. Calculate the Angle of Rotation:
- The angle of rotation for a regular polygon can be found by dividing 360 degrees by the order of rotational symmetry.
- For our regular octagon, we have 8 sides (or 8 rotations to return to the same position).
- Therefore, the angle of rotation is calculated by dividing 360 degrees by 8.
[tex]\[
\text{Angle of rotation} = \frac{360^\circ}{8} = 45^\circ
\][/tex]
Given these detailed steps, the order of rotational symmetry for a regular octagon is [tex]\(8\)[/tex], and the angle of rotation is [tex]\(45^\circ\)[/tex].
So, the correct answer is:
- Order [tex]\(= 8\)[/tex]
- Angle of rotation [tex]\(= 45^\circ\)[/tex]
