Question

1. the measures of consecutive interior angles when a transversal cuts through parallel lines are:

a. equal
b. complementary
c. vertical
d. supplementary

Explanation:

When a transversal cuts through parallel lines, by the consecutive interior angles theorem, the sum of consecutive interior angles is \(180^{\circ}\). Angles whose sum is \(180^{\circ}\) are called supplementary angles.

• Option a: Equal angles would imply each is \(90^{\circ}\) (if sum is \(180^{\circ}\)), but consecutive interior angles are not always \(90^{\circ}\) each.
• Option b: Complementary angles sum to \(90^{\circ}\), which is not the case here.
• Option c: Vertical angles are opposite angles formed by two intersecting lines, not related to consecutive interior angles.

Answer:

d. Supplementary