Question

two parallel lines, s and t, are cut by the transversal k as shown. suppose m∠1 = 50°.

Explanation:

Step1: Find the measure of ∠2

∠1 and ∠2 are vertical angles. Vertical angles are equal.
So, \(m\angle2 = m\angle1=50^{\circ}\)

Step2: Find the measure of ∠3

∠2 and ∠3 are same - side interior angles. Since \(s\parallel t\), same - side interior angles are supplementary (\(m\angle2 + m\angle3=180^{\circ}\))
Substitute \(m\angle2 = 50^{\circ}\) into the equation: \(50^{\circ}+m\angle3 = 180^{\circ}\)
Solve for \(m\angle3\): \(m\angle3=180^{\circ}- 50^{\circ}=130^{\circ}\)

Answer:

\(m\angle2 = 50^{\circ}\) and \(m\angle3 = 130^{\circ}\)