Question

in the figure below, ( mangle4 = 98^{circ} ). find ( mangle1 ), ( mangle2 ), and ( mangle3 ).

Explanation:

Step1: Find \( m\angle1 \)

Vertical angles are equal. \( \angle1 \) and \( \angle4 \) are supplementary (they form a linear pair). So \( m\angle1=180^{\circ}-m\angle4 \).
Since \( m\angle4 = 98^{\circ} \), then \( m\angle1=180 - 98=82^{\circ} \).

Step2: Find \( m\angle2 \)

\( \angle2 \) and \( \angle4 \) are vertical angles. Vertical angles are equal. So \( m\angle2=m\angle4 = 98^{\circ} \).

Step3: Find \( m\angle3 \)

\( \angle3 \) and \( \angle1 \) are vertical angles. Vertical angles are equal. So \( m\angle3=m\angle1 = 82^{\circ} \).

Answer:

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