Final answer:
The measure of angle M'N'O', after a 180-degree counterclockwise rotation, remains equal to the original measure of angle MNO, which is represented by option D. m∠M'N'O' = m∠MNO.
Step-by-step explanation:
The question asks us to determine the measure of angle M'N'O' after angle MNO is rotated 180 degrees counterclockwise about the origin. A rotation, especially one of 180 degrees, does not change the measure of the angle. Therefore, regardless of the rotation direction or pivot point, the measure of the angle remains the same after a full 180-degree rotation.
The correct statement that shows the measure of angle M'N'O' after the rotation would be D. m∠M'N'O' = m∠MNO.
Rotations in geometry are transformations that pivot a figure around a fixed point without altering its shape or size, which includes maintaining the measures of angles. In this case, the rotation does not affect the size of angle MNO, hence the sizes of MNO and M'N'O' are equal.