Question

parallel lines cut by a transversal
what is the measure of ∠1?

Explanation:

Step1: Use properties of parallel lines and transversals

When two parallel lines are cut by a transversal, the sum of consecutive - interior angles is \(180^{\circ}\). Also, vertical angles are equal. The angle of \(92^{\circ}\) and \(\angle2\) are consecutive - interior angles. So, \(\angle2 + 92^{\circ}=180^{\circ}\).

Step2: Solve for \(\angle2\)

\(\angle2=180^{\circ}-92^{\circ}=88^{\circ}\).

Step3: Use the property of vertical angles

\(\angle1\) and \(\angle2\) are vertical angles. Since vertical angles are equal, \(\angle1 = \angle2\).

Answer:

\(88^{\circ}\)