Question

in the figure below, ( mangle3 = 32^{circ} ). find ( mangle1 ), ( mangle2 ), and ( mangle4 ).

Explanation:

Step1: Vertical angles

Vertical angles are equal. So, \(m\angle1 = m\angle3\). Given \(m\angle3 = 32^{\circ}\), then \(m\angle1=32^{\circ}\).

Step2: Linear - pair angles

Angles in a linear pair are supplementary (\(m\angle1 + m\angle2=180^{\circ}\)). Since \(m\angle1 = 32^{\circ}\), then \(m\angle2=180^{\circ}-32^{\circ}=148^{\circ}\).

Step3: Vertical angles again

Since \(m\angle4 = m\angle2\) (vertical angles), then \(m\angle4 = 148^{\circ}\).

Answer:

\(m\angle1 = 32^{\circ}\), \(m\angle2 = 148^{\circ}\), \(m\angle4 = 148^{\circ}\)