Question

question 25 of 25 if every pair of consecutive angles of a quadrilateral are supplementary, then the quadrilateral must be a parallelogram. a. true b. false

Explanation:

Step1: Recall parallelogram property

In a parallelogram, opposite - sides are parallel.

Step2: Use property of parallel lines

When two parallel lines are cut by a transversal, consecutive interior angles are supplementary. In a parallelogram, adjacent (consecutive) angles are like consecutive interior angles formed by parallel sides and a side as a transversal. So, if in a quadrilateral every pair of consecutive angles are supplementary, then the opposite sides are parallel, and by the definition of a parallelogram (a quadrilateral with both pairs of opposite - sides parallel), the quadrilateral is a parallelogram.

Answer:

A. True