Question

the measures of consecutive interior angles when a transversal cuts through parallel lines are: a. equal b. vertical c. complementary d. supplementary

Explanation:

Step1: Recall the property of consecutive interior angles

When a transversal cuts through parallel lines, consecutive interior angles are supplementary. That is, their sum is \(180^{\circ}\).

Step2: Analyze each option

• Option A: Equal. This is not the case for consecutive interior angles. Equal angles would imply \(x = y\), but consecutive interior angles sum to \(180^{\circ}\) (not necessarily equal).
• Option B: Vertical. Vertical angles are a different pair of angles (opposite each other when two lines intersect). Consecutive interior angles are not vertical angles.
• Option C: Complementary. Complementary angles sum to \(90^{\circ}\). But consecutive interior angles sum to \(180^{\circ}\).
• Option D: Supplementary. This matches the property that consecutive interior angles formed by a transversal and parallel lines sum to \(180^{\circ}\).

Answer:

D. Supplementary