Question

1. given that parallel lines k and j are cut by transversal l and \\( \angle 1 = 140 ^ { \circ } \\), find the measure of angle 3

a \\( 140 ^ { \circ } \\)
b \\( 40 ^ { \circ } \\)
c \\( 50 ^ { \circ } \\)
d \\( 60 ^ { \circ } \\)

Explanation:

Step1: Find the measure of ∠2

Since ∠1 and ∠2 are supplementary angles (they form a linear pair), we use the formula \( \angle1+\angle2 = 180^{\circ}\). Given \( \angle1 = 140^{\circ}\), then \(140^{\circ}+\angle2=180^{\circ}\), so \( \angle2=180^{\circ}-140^{\circ}=40^{\circ}\).

Step2: Use the property of vertical angles

Vertical angles are equal. ∠3 and ∠2 are vertical angles. So \( \angle3=\angle2\).

Answer:

B. \(40^{\circ}\)