Question

two parallel lines are cut by a transversal as shown below. suppose ( mangle6 = 148^{circ}). find ( mangle1 ) and ( mangle3 ).

Explanation:

Step1: Find \(m\angle1\)

\(\angle1\) and \(\angle2\) are supplementary (\(\angle1+\angle2 = 180^{\circ}\)), \(\angle2\) and \(\angle6\) are corresponding angles (\(\angle2=\angle6\)). Given \(m\angle6 = 148^{\circ}\), so \(m\angle2=148^{\circ}\). Then \(m\angle1=180^{\circ}-m\angle2 = 180^{\circ}-148^{\circ}=32^{\circ}\).

Step2: Find \(m\angle3\)

\(\angle3\) and \(\angle6\) are alternate - interior angles. When two parallel lines are cut by a transversal, alternate - interior angles are equal. So \(m\angle3 = m\angle6=148^{\circ}\).

Answer:

\(m\angle1 = 32^{\circ}\), \(m\angle3 = 148^{\circ}\)