Which lines can you conclude are parallel given that m14 + m2 = 180? justify your conclusion with a theorem.

Option 2 is correct.

Step-by-step explanation:

Given the diagram and also the condition  m∠14 + m∠2 = 180°

we have to tell which lines are parallel.

By the theorem of exterior angles

Same-side exterior angles which are formed outside of the parallel lines and on same side of transversal line.

The theorem states that when parallel lines are cut by a transversal line, the sum of the same-side exterior angles is 180° i.e these are supplementary.

∴ Lines a and b are are parallel by converse of same side exterior angle theorem.