Question

two parallel lines are cut by a transversal as shown below. suppose ( m angle 4 = 124 ^ { circ } ). find ( m angle 5 ) and ( m angle 7 ).

Explanation:

Step1: Find \(m\angle5\)

Since \(\angle4\) and \(\angle5\) are same - side interior angles, and the two lines are parallel.
We know that same - side interior angles are supplementary. So \(m\angle4 + m\angle5=180^{\circ}\).
Given \(m\angle4 = 124^{\circ}\), then \(m\angle5=180^{\circ}-124^{\circ}=56^{\circ}\).

Step2: Find \(m\angle7\)

Since \(\angle5\) and \(\angle7\) are vertical angles.
Vertical angles are equal. So \(m\angle7 = m\angle5\).
Since \(m\angle5 = 56^{\circ}\), then \(m\angle7=56^{\circ}\).

Answer:

\(m\angle5 = 56^{\circ}\), \(m\angle7 = 56^{\circ}\)