Question

in the figure below, ( m angle 4 = 98^circ ). find ( m angle 1 ), ( m angle 2 ), and ( m angle 3 ).

Explanation:

Step1: Use vertical angles property

Vertical angles are equal. So, \(m\angle1 = m\angle3\) and \(m\angle2 = m\angle4\). Given \(m\angle4 = 98^{\circ}\), so \(m\angle2=98^{\circ}\).

Step2: Use linear - pair property

\(\angle1\) and \(\angle4\) form a linear pair. So \(m\angle1+m\angle4 = 180^{\circ}\). Substitute \(m\angle4 = 98^{\circ}\) into the equation: \(m\angle1=180^{\circ}-98^{\circ}\).

$$m\angle1 = 82^{\circ}$$

Since \(m\angle1 = m\angle3\), then \(m\angle3 = 82^{\circ}\).

Answer:

\(m\angle1 = 82^{\circ}\), \(m\angle2 = 98^{\circ}\), \(m\angle3 = 82^{\circ}\)