Question

in the figure below, ( mangle4 = 72^{circ} ). find ( mangle1 ), ( mangle2 ), and ( mangle3 ).

Explanation:

Step1: Vertical angles

Vertical angles are equal. So \(m\angle3 = m\angle4\). Since \(m\angle4 = 72^{\circ}\), then \(m\angle3=72^{\circ}\).

Step2: Linear - pair angles

Angles in a linear pair are supplementary (\(m\angle1 + m\angle4=180^{\circ}\)). Given \(m\angle4 = 72^{\circ}\), then \(m\angle1=180^{\circ}-72^{\circ}=108^{\circ}\).

Step3: Vertical angles

Since \(m\angle1\) and \(m\angle2\) are vertical angles, \(m\angle2 = m\angle1\). So \(m\angle2 = 108^{\circ}\).

Answer:

\(m\angle1 = 108^{\circ}\), \(m\angle2 = 108^{\circ}\), \(m\angle3 = 72^{\circ}\)