I need help with proofs

Question

Given: ∠1 and ∠2 

form a linear pair. 

m∠1 + m∠3 = 180 

Prove: ∠2 ≅ ∠3 

Answer 1

Given: ∠1 and ∠2 

form a linear pair. 

m∠1 + m∠3 = 180 

Two angles are said to be linear pairs if they are adjacent angles formed by two intersecting lines. By the definition of adjacent angles, they are supplementary since they combine to form a straight angle (180 degrees). Since ∠1 and ∠2 form a linear pair, they must be supplementary, so m∠1 + m∠2 = 180. By the subtraction property of equality, m∠1 = 180 - m∠2. We are also given that m∠1 + m∠3 = 180. By the subtraction property of equality, m∠1 = 180 - m∠2. By the transitive property, 180 - m∠2 = 180 - m∠3. By the subtraction property of equality, -m∠2 = -m∠3. By the multiplication property of equality, m∠2 = m∠3. By the definition of congruence, ∠2 ≅ ∠3.