Vertical angles are formed when two lines intersect, and they are the angles that are opposite each other. In your case, the given angles are:
- \( m\angle 1 = 32^\circ \)
- \( m\angle 2 = 148^\circ \)
- \( m\angle 3 = 32^\circ \)
- \( m\angle 4 = 148^\circ \)
The vertical angles are as follows:
- \( \angle 1 \) and \( \angle 3 \) are vertical angles.
- \( \angle 2 \) and \( \angle 4 \) are vertical angles.
The angle that is a vertical angle with \( \angle 2 \) (which measures \( 148^\circ \)) is \( \angle 4 \).
So, the vertical angle with \( \angle 2 \) is \( \angle 4 \).