Question

two parallel lines are cut by a transversal as shown below. suppose m ∠ 2 = 128°. find m ∠ 5 and m ∠ 7.

Explanation:

Step1: Find \( m\angle5 \)

\(\angle2\) and \(\angle5\) are same - side interior angles. When two parallel lines are cut by a transversal, same - side interior angles are supplementary, i.e., their sum is \(180^{\circ}\).
Given \(m\angle2 = 128^{\circ}\), we use the formula \(m\angle2+m\angle5=180^{\circ}\).
So, \(m\angle5 = 180^{\circ}-m\angle2=180 - 128=52^{\circ}\).

Step2: Find \( m\angle7 \)

\(\angle5\) and \(\angle7\) are vertical angles. Vertical angles are equal.
Since \(m\angle5 = 52^{\circ}\), then \(m\angle7=m\angle5 = 52^{\circ}\).

Answer:

\(m\angle5=\boldsymbol{52}^{\circ}\), \(m\angle7=\boldsymbol{52}^{\circ}\)