Question

if lines / and m are parallel, and d6 = 115^0, which is d4?
a. 45°
b. 65°
c. 85°
d. 115°

Explanation:

Step1: Find the measure of \(\angle5\)

Since \(\angle6 = 115^{\circ}\) and \(\angle5+\angle6=180^{\circ}\) (linear - pair), then \(\angle5 = 180^{\circ}-115^{\circ}=65^{\circ}\).

Step2: Use the property of parallel lines

Lines \(l\) and \(m\) are parallel. \(\angle4\) and \(\angle5\) are alternate - interior angles. Alternate - interior angles are equal when two parallel lines are cut by a transversal. So \(\angle4=\angle5 = 65^{\circ}\).

Answer:

B. \(65^{\circ}\)