Question

two parallel lines are cut by a transversal as shown below. suppose ( mangle7 = 142^{circ}). find ( mangle2 ) and ( mangle4 ).

Explanation:

Step1: Find \(m\angle 2\)

\(\angle 7\) and \(\angle 5\) are supplementary (\(\angle 5+\angle 7 = 180^{\circ}\)). So, \(\angle 5=180^{\circ}- 142^{\circ}=38^{\circ}\). \(\angle 2\) and \(\angle 5\) are corresponding angles (parallel lines cut by transversal). So, \(m\angle 2 = 38^{\circ}\).

Step2: Find \(m\angle 4\)

\(\angle 7\) and \(\angle 4\) are alternate interior angles (parallel lines cut by transversal). So, \(m\angle 4=m\angle 7 = 142^{\circ}\).

Answer:

\(m\angle 2 = 38^{\circ}\), \(m\angle 4 = 142^{\circ}\)