Question

two parallel lines are cut by a transversal as shown below. suppose ( m angle 2 = 128^{circ} ). find ( m angle 5 ) and ( m angle 8 ).

Explanation:

Step1: Find \(m\angle5\)

Since \(\angle2\) and \(\angle5\) are same - side interior angles. But wait, no! \(\angle2\) and \(\angle3\) are supplementary (\(\angle2+\angle3 = 180^{\circ}\), linear - pair). Then \(\angle3=180^{\circ}-128^{\circ}=52^{\circ}\). And \(\angle3\) and \(\angle5\) are alternate - interior angles. For parallel lines cut by a transversal, alternate - interior angles are equal. So \(m\angle5 = 52^{\circ}\).

Step2: Find \(m\angle8\)

\(\angle2\) and \(\angle8\) are corresponding angles. For parallel lines cut by a transversal, corresponding angles are equal. So \(m\angle8=128^{\circ}\).

Answer:

\(m\angle5 = 52^{\circ}\), \(m\angle8 = 128^{\circ}\)