Question

in the diagram, a || b. what is m∠1? a. 45° b. 55° c. 95° d. 125°

Explanation:

Step1: Find the supplementary angle

When two parallel lines are cut by a transversal, the consecutive interior angles are supplementary. The angle adjacent to \(125^{\circ}\) (let's call it \(x\)) satisfies \(x + 125^{\circ}=180^{\circ}\). So \(x = 180^{\circ}- 125^{\circ}=55^{\circ}\).

Step2: Use the property of alternate - interior angles

Since \(a\parallel b\), \(\angle1\) and \(x\) are alternate - interior angles. Alternate - interior angles are equal when two parallel lines are cut by a transversal. So \(m\angle1=x = 55^{\circ}\).

Answer:

B. \(55^{\circ}\)