Two lines parallel to the same plane are parallel to each other.

Through a point not on a line, one can always draw a line parallel to the given line.

Parallel lines are cut by a transversal such that the alternate interior angles have measures of (3x+17) and(x+53)degrees. So (3x+17)=(x+53)
3x+17=x+53
Using transposition method-
3x-x=53-17
2x=36
x=36/2
x=18

You can conclude that lines l and m are parallel by Alternate interior angles theorem.