Question

two parallel lines, w and v, are crossed by two transversals.
what is the measure of ∠5?
enter your answer in the box.

m∠5 = □°

Explanation:

Step1: Use the property of parallel lines and transversals

When two parallel lines \(w\) and \(v\) are cut by a transversal \(f\), consecutive interior angles are supplementary. But here, \(\angle3\) and the given \(78^{\circ}\) angle are adjacent and form a linear - pair. Also, \(\angle3\) and \(\angle5\) are alternate interior angles.
Since \(\angle3 + 78^{\circ}=180^{\circ}\) (linear - pair), then \(\angle3 = 180^{\circ}-78^{\circ}=102^{\circ}\).

Step2: Apply the alternate - interior angles theorem

For parallel lines \(w\) and \(v\) cut by transversal \(f\), alternate interior angles are equal. So \(m\angle5=m\angle3\).

Answer:

\(102\)