Question

given that parallel lines k and j are cut by transversal l and ∠1 = 140°, find the measure of angle 8
a. 140°
b. 40°
c. 50°
d. 60°

Explanation:

Step1: Find the measure of ∠4

Since ∠1 and ∠4 are vertical angles, they are equal. So, ∠4 = ∠1 = 140°.

Step2: Find the measure of ∠5

Since lines \(k\) and \(j\) are parallel and \(l\) is a transversal, ∠4 and ∠5 are same - side interior angles. So, ∠4+∠5 = 180°. Then ∠5=180° - ∠4 = 180° - 140° = 40°.

Step3: Find the measure of ∠8

Since ∠5 and ∠8 are vertical angles, they are equal. So, ∠8 = ∠5 = 40°.

Answer:

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