Question

Angle MNO is formed by segments MN and NO on the coordinate grid.

Angle MNO is rotated 90 degrees counterclockwise about the origin to form angle M′N′O′. Which statement shows the measure of angle M′N′O′?

A) m∠ M′N′O′ = 90 degrees
B) m∠ M′N′O′ = 180 degrees
C) m∠ M′N′O′ = 2 ⋅ m∠MNO
D) m∠ M′N′O′ = m∠MNO

Answer 1

The correct answer is D.

Answer 2

The correct option is D.

Explanation:

From the given figure it is clear that angle MNO is formed by segments MN and NO.

It is given that angle MNO is rotated 90 degrees counterclockwise about the origin to form angle M′N′O′.

Rotation is a rigid transformation because the size and shape of image is same as the figure after rotation. In other words, after rotation the figure and its image are congruent.

`m\angle MNO\cong m\angle M'N'O'` (Rigid transformation)

`m\angle MNO=m\angle M'N'O'` (Definition of congruence)

Since the measure of angle MNO is equal to the measure of angle M'N'O', therefore the correct option is D.