Are you given that angle 1 is congruent to angle 3 or are you supposed to prove that in addition to proving angle 2 is congruent to angle 4? It also helps to know what theorems/proofs you have been given because those are the ones you are expected to use in this case. Is there a picture that goes with this question? You need to describe it if there is one.
Here is a pdf that I have found very useful - it has a list of theorems, postulates, and definitions, with a place where you can write your own clues to help you remember how to use them. http://www.ouchihs.org/ourpages/auto/2013/7/26/52822673/Geo-PostulatesTheorems-List.pdf
If you fill out the "visual clue" part each time you learn a new theorem, postulate or definition in class, you will know which ones can be used for your proofs.
Your two column proof would start out with what you are given (EVERY proof starts with something you are given - could be all of it or only part of what was given) I am going to write the proof assuming you are given that angle 1 is congruent to angle 3. If that isn't true, I don't know of any way to solve the problem (unless you have a picture)
angle 1 is supplementary to angle 2 Given
m ∠1 + m ∠2 = 180 Definition of supplementary
angle 3 is supplementary to angle 4 Given
m ∠3 + m ∠4 = 180 Definition of supplementary
m ∠1 + m ∠2 = m ∠3 + m ∠4 Transitive property of equality
∠1 ≅ ∠3 Given or from picture
m ∠1 = m ∠3 Definition of congruence
m ∠1 + m ∠2 = m ∠1 + m ∠4 substitution property of equality
m ∠2 = m ∠4 subtraction property
∠2 ≅ ∠4 definition of congruence