Question

Luisa draws a regular nonagon and rotates it about its center. which angle measures can luisa rotate the regular nonagon through to map it onto itself? select each correct answer. 40° 80° 90° 120° 160° 180°

Answer 1

Answer: $40^{\circ}$

Step-by-step explanation:

Given: A regular nonagon with 9 sides.

For a regular nonagon, it maps onto itself 9 times during a rotation of 360°.

Mow, the angle at Lusia can rotate the regular nonagon through to map it onto itself=$\frac{360}{\text{number of sides of regular polygon}}=\frac{360}{9}=40^{\circ}$

• A shape is said to has rotational symmetry if it maps onto itself under rotation about a point at its center.
• The order of rotational symmetry is the number of times the shape maps onto itself during a rotation of 360°.

Answer 2

A shape that maps onto itself after rotation, has a rotation symmetry

The angles of rotation that would map the nonagon onto itself are:

$\mathbf{40, 80, 120\ and\ 160}$

A regular nonagon has nine equal sides i.e.

$\mathbf{n = 9}$

The angle at the center of the nonagon is:

$\mathbf{\theta = 360}$

So, the angle of rotation symmetry is:

$\mathbf{\alpha = \frac{\theta}{n}}$

This gives:

$\mathbf{\alpha = \frac{360}{9}}$

$\mathbf{\alpha = 40}$

This means that, the nonagon would map onto itself, when rotated at 40 degrees.

Other angles of rotation symmetry must be a multiple of 40

i.e.

$\mathbf{\alpha = 40, 80, 120, 160, 200, 240, 280......}$

Using the above list of angles, the angles of rotation that would map the nonagon onto itself are:

$\mathbf{40, 80, 120\ and\ 160}$

Read more about rotational symmetry at:

https://brainly.com/question/1597409