Question

given that parallel lines ( k ) and ( j ) are cut by transversal ( l ) and ( angle 1 = 140^{circ} ), find the measure of: angle 6
a. ( 140^{circ} )
b. ( 40^{circ} )
c. ( 50^{circ} )
d. ( 60^{circ} )

Explanation:

Step1: Find the measure of ∠3

∠1 and ∠3 are vertical angles. Vertical angles are equal. But wait, no! Wait, ∠1 and ∠3 are actually not vertical angles. Wait, ∠1 and ∠4 are supplementary (linear pair). ∠1 + ∠4=180°, so ∠4 = 180° - 140°=40°. Then, since k ∥ j and l is a transversal, ∠4 and ∠6 are alternate - interior angles. Alternate - interior angles are equal when two parallel lines are cut by a transversal.

Answer:

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