Question

in the figure below, ( mangle4 = 104^{circ} ). find ( mangle1 ), ( mangle2 ), and ( mangle3 ).

Explanation:

Step1: Find \(m\angle3\)

Vertical angles are equal. \(\angle3\) and \(\angle4\) are supplementary (\(\angle3+\angle4 = 180^{\circ}\)).
Since \(m\angle4=104^{\circ}\), then \(m\angle3=180^{\circ}- 104^{\circ}=76^{\circ}\).

Step2: Find \(m\angle1\)

Vertical angles are equal. \(\angle1\) and \(\angle4\) are vertical angles. So \(m\angle1 = m\angle4 = 104^{\circ}\).

Step3: Find \(m\angle2\)

Vertical angles are equal. \(\angle2\) and \(\angle3\) are vertical angles. So \(m\angle2=m\angle3 = 76^{\circ}\).

Answer:

\(m\angle1 = 104^{\circ}\), \(m\angle2 = 76^{\circ}\), \(m\angle3 = 76^{\circ}\)