Question

given that lines a and b are parallel and that ( mangle5 = 120^{circ} ), find ( mangle1 ).

Explanation:

Step1: Find \(m\angle3\)

Since \(m\angle5 = 120^{\circ}\), and \(\angle3\) and \(\angle5\) are alternate - interior angles (when two parallel lines \(a\) and \(b\) are cut by a transversal). Alternate - interior angles are equal. So \(m\angle3=m\angle5 = 120^{\circ}\).

Step2: Find \(m\angle1\)

\(\angle1\) and \(\angle3\) are supplementary angles (they form a linear pair). The sum of angles in a linear pair is \(180^{\circ}\). So \(m\angle1=180^{\circ}-m\angle3\). Substitute \(m\angle3 = 120^{\circ}\) into the formula: \(m\angle1=180^{\circ}- 120^{\circ}=60^{\circ}\).

Answer:

B. \(60^{\circ}\)