Question

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

Explanation:

Step1: Find \(m\angle6\)

Since \(\angle5\) and \(\angle6\) are supplementary (\(\angle5+\angle6 = 180^{\circ}\)), and \(m\angle5=120^{\circ}\), then \(m\angle6=180^{\circ}- 120^{\circ}=60^{\circ}\).

Step2: Use the property of parallel lines

Lines \(a\) and \(b\) are parallel. \(\angle1\) and \(\angle6\) are corresponding angles. Corresponding angles of parallel lines are equal. So \(m\angle1 = m\angle6\).

Answer:

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