Question

given that parallel lines k and j are cut by transversal l and \\( \angle 1 = 140 ^ { \circ } \\), find the measure of: angle 7

Explanation:

Step1: Find the measure of ∠3

∠1 and ∠3 are vertical angles. Vertical angles are equal. But wait, no! ∠1 and ∠3 are actually not vertical angles. ∠1 and ∠2 form a linear - pair. Since ∠1 = 140°, and ∠1+∠2 = 180° (linear - pair of angles), then ∠2=180° - 140° = 40°. Also, ∠2 and ∠3 are vertical angles, so ∠3 = ∠2 = 40°.

Step2: Use the property of parallel lines

Since lines \(k\) and \(j\) are parallel and \(l\) is a transversal, ∠3 and ∠7 are alternate - exterior angles. Alternate - exterior angles formed by parallel lines and a transversal are equal. So ∠7=∠3.

Answer:

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