Question

given the following information, determine which lines, if any, are parallel. state the converse that justifies your answer. measure angle 20 + measure angle 21 = 180 parallel lines =

Explanation:

Step1: Recall parallel - line theorem

If the sum of two consecutive interior angles formed by a transversal intersecting two lines is 180°, then the two lines are parallel. Angle 20 and angle 21 are consecutive interior angles formed by a transversal intersecting lines \(a\) and \(b\).

Step2: Determine parallel lines

Since measure of angle 20+ measure of angle 21 = 180°, by the converse of the consecutive - interior angles theorem, lines \(a\) and \(b\) are parallel. The converse of the consecutive - interior angles theorem states that if two lines are cut by a transversal so that a pair of consecutive interior angles are supplementary (sum to 180°), then the two lines are parallel.

Answer:

Lines \(a\) and \(b\) are parallel. The converse that justifies this answer is the converse of the consecutive - interior angles theorem.