Question

in the figure below, ( mangle a = 103^{circ} ), find ( mangle 1 ), ( mangle 2 ), and ( mangle 3 ).

Explanation:

Step1: Vertical angles property

Vertical angles are equal. So \(m\angle1 = m\angle A\).
Since \(m\angle A=103^{\circ}\), then \(m\angle1 = 103^{\circ}\).

Step2: Supplementary angles property

\(\angle1\) and \(\angle2\) are supplementary (\(\angle1+\angle2 = 180^{\circ}\)).
So \(m\angle2=180^{\circ}-m\angle1\).
Substitute \(m\angle1 = 103^{\circ}\), then \(m\angle2=180 - 103=77^{\circ}\).

Step3: Vertical angles property

\(\angle2\) and \(\angle3\) are vertical angles.
So \(m\angle3=m\angle2 = 77^{\circ}\).

Answer:

\(m\angle1 = 103^{\circ}\), \(m\angle2 = 77^{\circ}\), \(m\angle3 = 77^{\circ}\)