Question

in the diagram, a || b. what is m∠2? a. 60° b. 80° c. 90° d. 120°

Explanation:

Step1: Use the property of adjacent angles

When two parallel lines are cut by a transversal, the sum of adjacent angles is \(180^{\circ}\). Let the angle adjacent to the \(60^{\circ}\) angle be \(x\). Then \(x + 60^{\circ}=180^{\circ}\), so \(x = 180^{\circ}- 60^{\circ}=120^{\circ}\).

Step2: Use the property of vertical angles

\(\angle2\) and \(x\) are vertical angles. Vertical angles are equal. So \(m\angle2=x\).

Answer:

D. \(120^{\circ}\)