Question

lines l, m, and n lie in a plane and are cut by a transversal, t. ∠1 is supplementary to ∠2, and ∠2 is supplementary to ∠3. which lines, if any, are parallel? m and n m and l none all three lines

Explanation:

Step1: Recall supplementary - angle property

If two angles are supplementary, their sum is 180°. Given ∠1 + ∠2=180° and ∠2 + ∠3 = 180°. Then ∠1=∠3 (since if a + b = c + b, then a = c by the subtraction property of equality).

Step2: Apply corresponding - angle postulate

∠1 and ∠3 are corresponding angles. According to the corresponding - angle postulate, if two lines are cut by a transversal and the corresponding angles are congruent, then the two lines are parallel. Here, lines m and n are cut by transversal t and ∠1 and ∠3 are corresponding angles and ∠1 = ∠3. So, m∥n.

Answer:

m and n