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: Identify the relationship between angles

Since lines \(w\) and \(v\) are parallel and cut by transversal \(f\), \(\angle5\) and \(\angle3\) are alternate interior angles. Also, \(\angle3\) and the \(78^{\circ}\) angle are vertical angles.

Step2: Use the property of vertical angles

Vertical angles are equal. So \(m\angle3 = 78^{\circ}\) (because \(\angle3\) and the \(78^{\circ}\) angle are vertical angles).

Step3: Use the property of alternate - interior angles

Alternate - interior angles formed by parallel lines are equal. Since \(w\parallel v\) and \(f\) is a transversal, \(m\angle5=m\angle3\).

Answer:

\(78\)