First, let's start with the Linear Pair Postulate.
This postulate states that if two angles form a linear pair, then they are supplementary.
This means the angles ∠2 and ∠3 are supplementary. Since ∠2 and ∠3 are supplementary, and ∠1 and ∠2 are also supplementary, therefore, ∠1 is equal to ∠3.
Then, by the Parallel Line Postulate*, those lines are parallel.
This Postulate states: "Two lines cut by a transversal are parallel IF AND ONLY IF corresponding angles are congruent."
