Question

given that the two parallel lines are cut by a transversal, and the measure of angle 2 is 50 degrees. find each of the missing angles. angle 1 = 130 degrees angle 3 = 130 degrees angle 5 = 50 degrees angle 6 = 50 degrees

Explanation:

Step1: Use vertical angles

Vertical angles are equal. Since \(\angle2 = 50^{\circ}\), then \(\angle4=\angle2 = 50^{\circ}\), \(\angle6=\angle4 = 50^{\circ}\) (alternate - interior angles for parallel lines \(m\) and \(l\) cut by transversal), \(\angle8=\angle6 = 50^{\circ}\) (vertical angles).

Step2: Use linear - pair relationship

\(\angle1\) and \(\angle2\) form a linear pair (\(\angle1+\angle2 = 180^{\circ}\)). So \(\angle1=180^{\circ}-\angle2=180 - 50=130^{\circ}\).
Since \(\angle1=\angle3\) (vertical angles), then \(\angle3 = 130^{\circ}\). Also, \(\angle5=\angle3 = 130^{\circ}\) (alternate - interior angles for parallel lines \(m\) and \(l\) cut by transversal), \(\angle7=\angle5 = 130^{\circ}\) (vertical angles).

Answer:

\(\angle1 = 130^{\circ}\), \(\angle3 = 130^{\circ}\), \(\angle5 = 50^{\circ}\), \(\angle6 = 50^{\circ}\)