Question

which set of equations is enough information to prove that lines c and d are parallel lines cut by transversal p?

m∠1 = 81° and m∠2 = 99°
m∠3 = 99° and m∠4 = 99°
m∠2 = 99° and m∠4 = 99°
m∠4 = 81° and m∠1 = 81°

Explanation:

Step1: Recall the properties of parallel lines and transversals

When two parallel lines are cut by a transversal, alternate - interior angles are equal. In the given figure, if \(m\angle2 = 99^{\circ}\) and \(m\angle4=99^{\circ}\), \(\angle2\) and \(\angle4\) are alternate - interior angles.

Step2: Apply the converse of the alternate - interior angles theorem

The converse of the alternate - interior angles theorem states that if two lines are cut by a transversal such that alternate - interior angles are equal, then the two lines are parallel.

Answer:

\(m\angle2 = 99^{\circ}\) and \(m\angle4 = 99^{\circ}\)