Describing Rotations

To find the measure of the angle of rotation of $ABCD$ about the origin, it is enough to compare one of the vertices of $ABCD$ and its corresponding image.

Let's compare $A$ and $A^{\prime }.$ Knowing that the center of rotation is the origin, we will first draw two segments from $A$ and $A^{\prime }$ to the origin. Then, we will determine the angle between the segments.

As we can see above, the segments form a straight angle. Therefore, the measure of the angle of rotation is $180^{\circ }.$