Question

Given: ∠H and ∠X are supplementary. Prove: l || n

Answer 1

I won't write out a formal proof; here's an outline.

H+X=180.  definition of supplementary
H+F=180   crossing lines
X=F           supplements of the same angle are equal, or just algebra          
l || n          When the alternate angles of a transverse line between two lines are congruent, the lines are parallel