Question

the diagram shows several parking spots near the grocery store, formed with three parallel line segments and a transversal. if the measure of ∠4 is 132°, what is the measure of ∠7?

Explanation:

Step1: Find the measure of ∠3

Since ∠4 and ∠3 are supplementary angles (they form a linear pair), we use the formula \( \angle3 = 180^{\circ}-\angle4 \).
Given \( \angle4 = 132^{\circ} \), then \( \angle3=180^{\circ}- 132^{\circ}=48^{\circ} \).

Step2: Find the measure of ∠7

Because the three line segments are parallel and we have a transversal, ∠3 and ∠7 are alternate - interior angles. Alternate - interior angles are equal when lines are parallel. So \( \angle7=\angle3 \).

Answer:

\(48^{\circ}\)