Two intersecting lines create four angles, numbered 1,2,3 and 4, where <4 is adjacent to <1 and <3 and m<2 = 110 . Which other angle has a measure that is also equal to 110 ?

Answer 1

When two lines intersect, they create pairs of vertical angles that are equal and adjacent angles that are supplementary (i.e., their measures add up to 180 degrees).

You mentioned that \( m\angle 2 = 110^\circ \).

1. Since angles 2 and 1 are adjacent, we can find the measure of angle 1: \[ m\angle 1 + m\angle 2 = 180^\circ \] \[ m\angle 1 + 110^\circ = 180^\circ \] \[ m\angle 1 = 180^\circ - 110^\circ = 70^\circ \]

2. Angles 2 and 4 are also adjacent, so: \[ m\angle 4 + m\angle 2 = 180^\circ \] \[ m\angle 4 + 110^\circ = 180^\circ \] \[ m\angle 4 = 180^\circ - 110^\circ = 70^\circ \]

3. Angles 2 and 3 are vertical angles, so: \[ m\angle 3 = m\angle 2 = 110^\circ \]

Thus, the angles with a measure equal to \( 110^\circ \) are \( \angle 2 \) and \( \angle 3 \). Therefore, the other angle that also has a measure of \( 110^\circ \) is \( \angle 3 \).