In Fig.6.6, which of the two lines are parallel and why?

In the 1^st figure –

Let the intersecting points of l and n be a, and of m and n be b respectively.

We have, ∠lab = 132°, ∠abm = 48° - - - - (i)

l is a ray on the line n. By linear pair axiom,

∠nal + ∠lab = 180°

⇒ ∠nal + 132° = 180°

⇒ ∠nal = 180° - 132°

⇒ ∠nal = 48° - - - - (ii)

Also, we have ∠abm = 48° from equation (i)

We can say that, the two corresponding angles,

∠abm = ∠nal = 48° - - - - (iii)

Since, the two corresponding angles are equal, such that a transversal n intersects two lines, then they are parallel to each other.