Question

question 5: two parallel lines are cut by a transversal suppose ( m angle 8 = 33^{circ} ). find ( m angle 2 ) and ( m angle 3 ) ( m angle 2= ) ( m angle 3= )

Explanation:

Step1: Find \(m\angle2\)

Since \(\angle2\) and \(\angle8\) are alternate - exterior angles. When two parallel lines are cut by a transversal, alternate - exterior angles are congruent. So \(m\angle2=m\angle8\). Given \(m\angle8 = 33^{\circ}\), then \(m\angle2=33^{\circ}\).

Step2: Find \(m\angle3\)

Since \(\angle2\) and \(\angle3\) are supplementary angles (they form a linear pair, \(\angle2+\angle3 = 180^{\circ}\)). We know \(m\angle2 = 33^{\circ}\). Then \(m\angle3=180^{\circ}-m\angle2\). Substitute \(m\angle2 = 33^{\circ}\) into the formula: \(m\angle3=180^{\circ}- 33^{\circ}=147^{\circ}\).

Answer:

\(m\angle2 = 33^{\circ}\), \(m\angle3=147^{\circ}\)