Question

in the figure below, ( mangle2 = 101^{circ} ). find ( mangle1 ), ( mangle3 ), and ( mangle4 ).

Explanation:

Step1: Find \(m\angle1\)

\(\angle1\) and \(\angle2\) are supplementary angles.
\(m\angle1 + m\angle2=180^{\circ}\)
Since \(m\angle2 = 101^{\circ}\), then \(m\angle1=180^{\circ}- 101^{\circ}=79^{\circ}\)

Step2: Find \(m\angle3\)

\(\angle2\) and \(\angle3\) are vertical angles.
Vertical angles are equal. So \(m\angle3=m\angle2 = 101^{\circ}\)

Step3: Find \(m\angle4\)

\(\angle1\) and \(\angle4\) are vertical angles.
Vertical angles are equal. So \(m\angle4=m\angle1 = 79^{\circ}\)

Answer:

\(m\angle1 = 79^{\circ}\), \(m\angle3 = 101^{\circ}\), \(m\angle4 = 79^{\circ}\)