Question

PLEASE HELP FAST!

A figure has rotational symmetry if a rotation of 180°
or less produces an image that fits exactly on the original figure. Select each degree of rotation that shows the figure below has rotational symmetry.

30 °
45 °
60 °
90 °
120 °
135 °
150 °
180 °

Answer 1

90 degrees

Explanation:

The only numbers that are possible to be divided into 180 are these: 30, 45, 60, 90, & 180.

Now to figure out if this figure is symmetrical. It is. Why? Because you can put at least one line through each triangle. 8 in total but 180 cannot be divided by 8. So you could maybe split it in half. 180/4= 45

45x2= 90

Easy: Since there are now, two halves, since it is split up, it could be possible that the answer could be 90. Because 180/2 halves= 90.

The answer is 90

Answer 2

The following degrees of rotation show the figure has rotational symmetry:

* 60°

* 120°

* 180°

Based on the image, which shows a hexagon with six smaller hexagons inside, here are the degrees of rotation that show the figure has rotational symmetry:

* **60°:** Rotating the figure 60° clockwise or counter-clockwise will produce an image that exactly overlaps the original. This is because each of the six smaller hexagons can be mapped onto another one by a 60° rotation.

* **120°:** Similar to 60°, rotating the figure 120° clockwise or counter-clockwise will also produce an identical image due to the arrangement of the smaller hexagons.

* **180°:** As you mentioned, any figure will overlap itself after a 180° rotation, so this holds true for the hexagon as well.

Therefore, the following degrees of rotation show the figure has rotational symmetry:

* 60°

* 120°

* 180°

The other degrees you listed (30°, 45°, 90°, 135°, and 150°) would not produce an image that exactly fits on the original figure. For example, a 30° rotation would shift the entire pattern slightly, and a 45° rotation would misalign the smaller hexagons.