Question

in the figure below, ( mangle1 = 126^{circ} ). find ( mangle2 ), ( mangle3 ), and ( mangle4 ).

Explanation:

Step1: Find \(m\angle2\)

\(\angle1\) and \(\angle2\) are supplementary angles.
\(m\angle1 + m\angle2=180^{\circ}\)
\(126^{\circ}+m\angle2 = 180^{\circ}\)
\(m\angle2=180^{\circ}- 126^{\circ}=54^{\circ}\)

Step2: Find \(m\angle3\)

\(\angle2\) and \(\angle3\) are supplementary angles.
\(m\angle2 + m\angle3=180^{\circ}\)
\(54^{\circ}+m\angle3 = 180^{\circ}\)
\(m\angle3=180^{\circ}-54^{\circ}=126^{\circ}\)

Step3: Find \(m\angle4\)

\(\angle3\) and \(\angle4\) are supplementary angles.
\(m\angle3 + m\angle4=180^{\circ}\)
\(126^{\circ}+m\angle4 = 180^{\circ}\)
\(m\angle4=180^{\circ}-126^{\circ}=54^{\circ}\)

Answer:

\(m\angle2 = 54^{\circ}\)
\(m\angle3 = 126^{\circ}\)
\(m\angle4 = 54^{\circ}\)