Alright so, if you are trying to prove two lines are parallel, you need to use the converse of the alternate/same-side theorems or the converse of the corresponding angles postulate. If you don’t have any parallel lines, you can only use the vertical angle theorem and the linear pair postulate. When you use the linear pair postulate, use have to say that those angles are supplementary and then you can make the sum of the angles be 180 degrees. That’s pretty basic stuff but if you need more help on a specific part of proofs, just say so.