Question

in the figure below, ( mangle1 = 32^{circ} ). find ( mangle2 ), ( mangle3 ), and ( mangle4 ).

Explanation:

Step1: Use the property of vertical angles

Vertical angles are equal. So, \(m\angle2 = m\angle4 = 148^{\circ}\) (This is incorrect in the original problem's partial answer. Wait, no, wait. Wait, \(\angle1\) and \(\angle3\) are supplementary to \(\angle4\) and \(\angle2\) respectively. Wait, no. Wait, \(\angle1\) and \(\angle3\) are adjacent and form a linear - pair (sum to \(180^{\circ}\)).
Since \(m\angle1 = 32^{\circ}\), and \(\angle1+\angle3=180^{\circ}\) (linear - pair of angles)

$$m\angle3=180 - m\angle1$$

$$m\angle3=180 - 32$$

$$m\angle3 = 148^{\circ}$$

Answer:

\(m\angle3 = 148^{\circ}\)