Question

Which lines are parallel if m<1 +m<2=180?

Answer 1

Answer is choice A) j || k by the Converse of the Same Side Interior Angles Theorem

Lines j and k are the upward slanted lines on the left and right respectively. The transversal we only care about is line k. Line g is extra info put in there most likely to throw you off.

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The Same Side Interior Angles Theorem says that if two lines are parallel, then the same side interior angles (formed by the transversal cut) are supplementary. Those two same side interior angles add to 180 degrees. The converse reverses the direction of the theorem.

The converse says that if we know the same side interior angles are supplementary, then it leads to the two parallel looking lines to actually being parallel. So this is one way to check parallel-ness of two lines.

Answer 2

Answer: A. l║k , by converse of the same side interior angles theorem.

Step-by-step explanation:

Same-side interior angle theorem : If two lines are parallel that are intersected by a transversal line then the sum of same-side interior angles are 180 degrees.

Converse of the same side interior angles theorem  :  If two lines are cut by a transversal and the consecutive interior angles are supplementary, then the lines are parallel.

In the given picture , we are given two lines l and k intersected by another two  transversal lines g and h.

∠1 and ∠2 are the consecutive interior angles formed on line l and k by transversal line h

If m∠1 + m∠2 = 180°

⇒  line l and k are parallel   [By converse of the same side interior angles theorem.]

Hence, the correct answer = A. l║k , by converse of the same side interior angles theorem.