Question

given that parallel lines ( k ) and ( j ) are cut by transversal ( l ) and ( angle 1 = 140^{circ} ), find the measure of: angle 3
a. ( 140^{circ} )
b. ( 40^{circ} )
c. ( 50^{circ} )
d. ( 60^{circ} )

Explanation:

Step1: Use the property of adjacent angles

Adjacent angles on a straight line sum to \(180^{\circ}\). So, \(\angle1+\angle3 = 180^{\circ}\)

Step2: Solve for \(\angle3\)

Given \(\angle1 = 140^{\circ}\), then \(\angle3=180^{\circ}-\angle1\)
Substitute \(\angle1 = 140^{\circ}\) into the formula: \(\angle3 = 180^{\circ}- 140^{\circ}=40^{\circ}\)

Answer:

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