Question

Four angles share a vertex m<1 = 32 , m<2 = 148 , m<3 = 32 , and m<4 = 148 . Which angle is a vertical angle with <2

Answer 1

Vertical angles are formed when two lines intersect, and they are opposite each other at the intersection. Vertical angles are equal.

Given the angles:
- \( m\angle 1 = 32^\circ \)
- \( m\angle 2 = 148^\circ \)
- \( m\angle 3 = 32^\circ \)
- \( m\angle 4 = 148^\circ \)

Since \( m\angle 2 = 148^\circ \), the vertical angle to \( \angle 2 \) would be the angle that shares the same vertex and is opposite \( \angle 2 \).

Looking at the given angles:
- \( \angle 4\) has the same measure as \( \angle 2\) (both are \( 148^\circ \)) and therefore is not vertical with it.
- \( \angle 3\) has the same measure as \( \angle 1\) but not \( \angle 2 \).

So, the angles \( 1 \) and \( 3 \) each measure \( 32^\circ \).

Given the angles:
- Vertical angles to \( \angle 2 \) is \( \angle 4 \), and since they share no equal measure, the correct answer would be \( \angle 1\) or \( \angle 3\), which are the vertical angles.

Thus, the angle that is a vertical angle with \( \angle 2 \) is \( \angle 4 \) as they are equal and opposites.