A rectangle has its center at the origin with two sides parallel to the x-axis and two sides parallel to the y-axis. It has side lengths 10 units and 6 units.Select all the rotation angles about the origin that map the rectangle onto itself.45°90°120°180°270°360°Submit

The rectangle will map onto itself if it is rotated by 90°, 180°, 270°, or 360° about the origin.

Here's why:

1. A 90° rotation will turn the rectangle so that the sides that were parallel to the x-axis are now parallel to the y-axis, and vice versa. The rectangle still covers the same area and is in the same position relative to the origin.

2. A 180° rotation will turn the rectangle upside down. The sides that were parallel to the x-axis are still parallel to the x-axis (and similarly for the y-axis), so the rectangle still covers the same area and is in the same position relative to the origin.

3. A 270° rotation is the same as a -90° rotation (or a 90° rotation in the opposite direction). This will again turn the rectangle so that the sides that were parallel to the x-axis are now parallel to the y-axis, and vice versa.

4. A 360° rotation is the same as no rotation at all. The rectangle remains exactly where it was.

On the other hand, a 45° or 120° rotation will not map the rectangle onto itself. These rotations will change the orientation of the rectangle so that its sides are no longer parallel to the x-axis or y-axis.