Question

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

Answer 1

Line a is parallel to line b by the Converse of the Same-Side Exterior Angles Theorem

because m<14 and m<2 are in lines a and b and they aren't corresponding angles

Answer 2

Option 2 is correct.

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.