Question

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.

Answer 1

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,

$\angle 1+\angle 2=180^{\circ}\ \ \ \ (\text{as they are supplementary angles})$

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

$\angle 2+\angle 3=180^{\circ}$

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.

Answer 2

Answer:

Step-by-step explanation:

M and N

Converse of same side interior angle theorem.