Question

two parallel lines are cut by a transversal as shown below. suppose $m\angle 4 = 128^{\circ}$. find $m\angle 6$ and $m\angle 7$.

Explanation:

Step1: Find \(m\angle6\)

When two parallel lines are cut by a transversal, \(\angle4\) and \(\angle6\) are same - side interior angles. The sum of same - side interior angles is \(180^{\circ}\).
So, \(m\angle4 + m\angle6=180^{\circ}\).
Given \(m\angle4 = 128^{\circ}\), then \(m\angle6=180^{\circ}-m\angle4\).
Substitute \(m\angle4 = 128^{\circ}\) into the formula: \(m\angle6 = 180^{\circ}-128^{\circ}=52^{\circ}\).

Step2: Find \(m\angle7\)

\(\angle6\) and \(\angle7\) are vertical angles. Vertical angles are equal.
Since \(m\angle6 = 52^{\circ}\), then \(m\angle7=m\angle6 = 52^{\circ}\).

Answer:

\(m\angle6 = 52^{\circ}\), \(m\angle7 = 52^{\circ}\)