Question

logical reasoning is it possible to prove that lines a and b are parallel? if so, explain how. 20. a b 37° 143°

Explanation:

Step1: Check angle - relationship

We know that if two lines are cut by a transversal, and the sum of two adjacent angles on the same - side of the transversal is 180°, then the two lines are parallel. Here, the two given angles 143° and 37° are adjacent angles on the same - side of the transversal.

Step2: Calculate the sum of the angles

$143^{\circ}+37^{\circ}=180^{\circ}$
Since the sum of the two adjacent angles on the same - side of the transversal is 180°, by the same - side interior angles postulate, lines a and b are parallel.

Answer:

Yes, since the sum of the adjacent angles on the same - side of the transversal (143° and 37°) is 180°, lines a and b are parallel by the same - side interior angles postulate.