Question

two parallel lines are cut by a transversal as shown below. suppose ( mangle4 = 148^{circ} ). find ( mangle6 ) and ( mangle7 ).

Explanation:

Step1: Find \(m\angle6\)

Since \(\angle4\) and \(\angle6\) are same - side interior angles.
For parallel lines cut by a transversal, same - side interior angles are supplementary.
So, \(m\angle4 + m\angle6=180^{\circ}\)
Given \(m\angle4 = 148^{\circ}\), then \(m\angle6=180^{\circ}-148^{\circ}=32^{\circ}\)

Step2: Find \(m\angle7\)

Since \(\angle6\) and \(\angle7\) are vertical angles.
Vertical angles are equal.
So, \(m\angle7 = m\angle6 = 32^{\circ}\)

Answer:

\(m\angle6 = 32^{\circ}\)
\(m\angle7 = 32^{\circ}\)