Question

2 given that parallel lines k and j are cut by transversal l and ∠1 = 140°, find the measure of angle 5 a 140° b 40° c 50° d 60°

Explanation:

Step1: Find the measure of ∠3

Since ∠1 and ∠3 are vertical angles, they are equal. So ∠3 = ∠1 = 140°.

Step2: Use the property of consecutive - interior angles

∠3 and ∠5 are consecutive - interior angles. For parallel lines \(k\) and \(j\) cut by transversal \(l\), consecutive - interior angles are supplementary. That is \(∠3+∠5 = 180^{\circ}\).
Substitute \(∠3 = 140^{\circ}\) into the equation: \(140^{\circ}+∠5=180^{\circ}\).
Solve for \(∠5\): \(∠5=180^{\circ}-140^{\circ}\).

Answer:

\(40^{\circ}\), so the answer is B.