Chapter 11.5, Problem 17HP

To determine

To determine rotational symmetry and the angle of rotation.

Explanation of Solution

Given:

Rotational symmetry

A figure is said to have rotational symmetry if its fits onto itself each time even after rotation. It will fits onto itself more than once during a full turn that is rotation through $360°$ .

Taking an example:

Suppose, take a Octagon,

  

If rotated the shape remains same and fits well,

  

So, it shares rotational symmetry property.

Now considering the line joining the mid points with the vertex,

There are total 8 intersection lines in the middle.

Total sum of angle in the middle is $360°$

Now, dividing $\frac{360°}{8}=45°$

So,

  

So, angle of rotation is $45°$ .