Answered

IDNLearn.com offers a seamless experience for finding and sharing knowledge. Find the information you need quickly and easily with our comprehensive and accurate Q&A platform.

What is the order of rotational symmetry and the angle of rotation for a regular octagon (8 sides)?

A. Order = 8, angle of rotation = [tex]$45^{\circ}$[/tex]
B. Order = 45, angle of rotation = [tex]$8^{\circ}$[/tex]
C. Order = 8, angle of rotation = [tex]$360^{\circ}$[/tex]
D. Order = 360, angle of rotation = [tex]$8^{\circ}$[/tex]

Sagot :

GinnyAnsweridn
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]
We greatly appreciate every question and answer you provide. Keep engaging and finding the best solutions. This community is the perfect place to learn and grow together. IDNLearn.com has the solutions to your questions. Thanks for stopping by, and come back for more insightful information.