Question

given that parallel lines b and j are cut by transversal f and ∠1 = 140°, find the measure of angle 6
a 140°
b 40°
c 100°
d 80°

Explanation:

Step1: Find the measure of the angle adjacent to ∠1

Since ∠1 and the angle adjacent to it form a linear - pair (sum to \(180^{\circ}\)), let the adjacent angle be \(x\). Then \(x = 180^{\circ}-\angle1\). Given \(\angle1 = 140^{\circ}\), so \(x=180 - 140=40^{\circ}\).

Step2: Use the property of alternate - interior angles

When two parallel lines \(h\) and \(j\) are cut by a transversal \(l\), the angle \(x\) (which we found to be \(40^{\circ}\)) and \(\angle6\) are alternate - interior angles. Alternate - interior angles are congruent. So \(\angle6=x\).

Answer:

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