Lines l, m, and n lie in a plane and are cut by a transversals, < 1 is supplementary to < 2, and < 2 is supplementary to < 3.

Step-by-step explanation:

M and N

Converse of same side interior angle theorem.

Answer-

According to converse same side interior angles theorem, line m and n are parallel.

Solution-

Lines l, m, and n lie in a plane and are cut by a transversal,

Also given that ∠2 and ∠3 are supplementary angles,

Consecutive Interior Angles-

The pairs of angles on one side of the transversal, but inside the two lines are called Consecutive Interior Angles.

Here, ∠2 and ∠3 are Consecutive Interior Angles.

Converse Consecutive/ same side Interior Angles Theorem-

The consecutive interior angles converse states that If two lines are cut by a transversal so that consecutive interior angles are supplementary, then the lines are parallel.

Therefore, line m and n are parallel.

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step-by-step explanation: