Question

in the figure below, ( mangle2 = 46^{circ} ). find ( mangle1 ), ( mangle3 ), and ( mangle4 ).

Explanation:

Step1: Vertical angles

Vertical angles are equal. So \(m\angle1 = m\angle3\) and \(m\angle2 = m\angle4\). Given \(m\angle2 = 46^{\circ}\), so \(m\angle4=46^{\circ}\).

Step2: Supplementary angles

\(\angle1\) and \(\angle2\) are supplementary (\(\angle1+\angle2 = 180^{\circ}\)). Since \(m\angle2 = 46^{\circ}\), then \(m\angle1=180^{\circ}- 46^{\circ}=134^{\circ}\).

Step3: Vertical angles (again)

Since \(m\angle1 = m\angle3\), so \(m\angle3 = 134^{\circ}\).

Answer:

\(m\angle1 = 134^{\circ}\), \(m\angle3 = 134^{\circ}\), \(m\angle4 = 46^{\circ}\)