Question

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

Explanation:

Step1: Find the adjacent angle of ∠1

When two parallel lines are cut by a transversal, ∠1 and its adjacent angle form a linear - pair. The sum of angles in a linear - pair is \(180^{\circ}\). Let the adjacent angle of ∠1 be \(x\). Then \(x + 140^{\circ}=180^{\circ}\), so \(x = 180^{\circ}-140^{\circ}=40^{\circ}\).

Step2: Use the property of corresponding angles

Since lines \(k\) and \(j\) are parallel and cut by a transversal, the angle \(x\) (which we found to be \(40^{\circ}\)) and angle \(\theta\) are corresponding angles. Corresponding angles are equal when two parallel lines are cut by a transversal.

Answer:

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