Question

in the figure below, ( m angle 1 = 37^{circ} ). find ( m angle 2 ), ( m angle 3 ), and ( m angle 4 ).

Explanation:

Step1: Find \( m\angle3 \) using vertical angles

Vertical angles are equal. Since \( \angle1 \) and \( \angle3 \) are vertical angles, \( m\angle3=m\angle1 = 37^{\circ}\).

Step2: Find \( m\angle2 \) using linear - pair

\(\angle1\) and \(\angle2\) form a linear pair (\(m\angle1 + m\angle2=180^{\circ}\)). So \(m\angle2 = 180^{\circ}-m\angle1\). Substitute \(m\angle1 = 37^{\circ}\), then \(m\angle2=180 - 37=143^{\circ}\).

Step3: Find \( m\angle4 \) using vertical angles

\(\angle2\) and \(\angle4\) are vertical angles. So \(m\angle4=m\angle2 = 143^{\circ}\).

Answer:

\(m\angle2 = 143^{\circ}\), \(m\angle3 = 37^{\circ}\), \(m\angle4 = 143^{\circ}\)