Question

Suppose both pairs of opposite sides of a quadrilateral are parallel. Which angles of the quadrilateral must be supplementary?

A) Pairs of opposite angles are complementary; the sides of the quadrilateral are transversals, and the interior angles on the same side of the transversal are not congruent.
B) Pairs of consecutive angles are supplementary; the sides of the quadrilateral are transversals, and the interior angles on the same side of the transversal are not congruent.
C) Pairs of opposite angles are supplementary; the sides of the quadrilateral are transversals, and the interior angles on the same side of the transversal are congruent.
D) Pairs of consecutive angles are complementary; the sides of the quadrilateral are transversals, and the interior angles on the same side of the transversal are congruent.

Answer 1

In a quadrilateral where both pairs of opposite sides are parallel, pairs of consecutive angles must be supplementary. Hence, option B) is correct.

Step-by-step explanation:

In a quadrilateral where both pairs of opposite sides are parallel, the angles that must be supplementary are pairs of consecutive angles (Option B: Pairs of consecutive angles are supplementary).

When opposite sides of a quadrilateral are parallel, it forms a special type of quadrilateral called a parallelogram. In a parallelogram, opposite angles are congruent (equal). Since consecutive angles are adjacent and do not share a side, they must add up to a straight angle, which is 180 degrees. Therefore, pairs of consecutive angles in a parallelogram are supplementary.

For example, if we have a parallelogram ABCD with angles ∠A, ∠B, ∠C, and ∠D, then ∠A + ∠B = 180 degrees and ∠C + ∠D = 180 degrees.