I need to solve a 2 column proof.

Question

So here is the situation: I have to give the statement and the reason to end up with the Proof. It is a 2 column proof and i'm supposed to be able to use any possible reason and i know one of them is "Definition of Supplementary Angles" but dunno the rest.

Given:

  ∠1 and ∠2 are supplementary angles.

  ∠3 and ∠4 are supplementary angles.

  ∠1 ≅∠4

 

Prove:

  ∠2 ≅ ∠3

 

I'm not too sure how to do this equation so if anyone can reply that will be greatly appreciated! :D

Answer 1

∠1 and ∠2 are supplementary angles            Given

∠3 and ∠4 are supplementary angles            Given

m∠1 +  m∠2  =  180                                        Definition of Supplementary Angles

m∠3  + m∠4  =  180                                        Definition of Supplementary Angles

m∠1  +  m∠2  =  m∠3  +  m∠4                         Transference Property of Equality

∠1  ≈  ∠4                                                        Given

m∠1  =  m∠4                                                   Definition of Congruence

m∠1  + m∠2  =   m∠3  +  m∠1                         Substitution

m∠2   =  m∠3                                                  Subtraction Property of Equality

∠2   ≈   ∠3                                                       Definition of Congruence