∠2 = ∠3 | Given
∠1 + ∠2 = 180 | Supplementary Angles Postule (If two angles are adjacent and ∠3 + ∠4 = 180| linear, they're supplementary)
∠1 + ∠2 = ∠3 + ∠4 | Transitive property
∠1 + ∠3 = ∠3 + ∠4 | Substitution property
∠1 = ∠4 | Subtraction Property
∠2 = ∠3 | Supplementary Congruent Theorem