Question

which set of equations is enough information to prove that lines a and b are parallel lines cut by transversal f?

m∠4 = 110° and m∠3 = 70°
m∠1 = 110° and m∠2 = 110°
m∠1 = 110° and m∠3 = 70°
m∠2 = 110° and m∠3 = 110°

Explanation:

Step1: Recall the properties of parallel lines and transversals

When two parallel lines are cut by a transversal, consecutive interior angles are supplementary (sum to \(180^{\circ}\)). \(\angle1\) and \(\angle3\) are consecutive interior angles.

Step2: Check the sum of angles

If \(m\angle1 = 110^{\circ}\) and \(m\angle3=70^{\circ}\), then \(m\angle1 + m\angle3=110^{\circ}+70^{\circ}=180^{\circ}\).

Answer:

\(m\angle1 = 110^{\circ}\) and \(m\angle3 = 70^{\circ}\) (the third option)