Answer-
According to converse same side interior angles theorem, line m and n are parallel.
Solution-
Lines l, m, and n lie in a plane and are cut by a transversal,
[tex]\angle 1+\angle 2=180^{\circ}\ \ \ \ (\text{as they are supplementary angles})[/tex]
Also given that ∠2 and ∠3 are supplementary angles,
[tex]\angle 2+\angle 3=180^{\circ}[/tex]
Consecutive Interior Angles-
The pairs of angles on one side of the transversal, but inside the two lines are called Consecutive Interior Angles.
Here, ∠2 and ∠3 are Consecutive Interior Angles.
Converse Consecutive/ same side Interior Angles Theorem-
The consecutive interior angles converse states that If two lines are cut by a transversal so that consecutive interior angles are supplementary, then the lines are parallel.
Therefore, line m and n are parallel.
