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