∠2 and ∠4 are a linear pair, so they are supplementary, regardless of lines l and m are parallel or not.
∠1 and ∠8 are alternate exterior angles since they are on the outer side of each line (l and m) but on the opposite side of the transversal line. If l and m are parallel lines, then the alternate exterior angles are equal, so ∠1=∠8
∠6 and ∠3 are alternate interior angles. If lines m and l are parallel, then these angles are congruent. The only case in which these equal angles will add up to 180º is if they are right angles.
∠7 and ∠6 are vertically opposite angles since they are opposite to each other when the two lines cross formin an X-shape. These angles are always equal.
The only fact that will allow you to prove that l and m are parallel is m∠1=m∠8