Question

If the figure has rotational symmetry, list the angles of rotation less than 360°. Enter the angles from least to greatest, separated by commas. If the figure does not have a rotational symmetry, enter the number zero. The list of angles of rotation is ??

Answer 1

45°,90°,135°,180°,225°,270°,315°

Explanation:

A figure possess rotational symmetry if it is rotated and still look the same as it did before the rotation.

The figure is an octagon and it has an angle of rotation of
`(360)/(8)=45` degrees

So, the rotational symmetry will occur at angles that are multiples of 45 degrees.

The angles will be :

45°,90°,135°,180°,225°,270°,315°

Answer 2

The angles of rotation less than 360° from least to greatest are

45°,90°,135°,180°,225°,270°,315°

Explanation:

we know that

The figure is a regular octagon

A regular octagon is a closed figure with eight sides of the same length and internal angles of the same size.

The angle of rotation would be 360 degrees divided by the order

The order of any regular polygon is the number of sides

An octagon is an eight-sided figure, so the order is eight

An octagon has an angle of rotation of 360/8=45 degrees

The angles of rotation will be

1) 45°

2) 2(45°)=90°

3) 3(45°)=135°

4) 4(45°)=180°

5) 5(45°)=225°

6) 6(45°)=270°

7) 7(45°)=315°

therefore

The angles of rotation less than 360° from least to greatest are

45°,90°,135°,180°,225°,270°,315°