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 vertical angles.
So \( m\angle1 = m\angle4 = 98^{\circ} \)

Step2: Find \( m\angle2 \)

\( \angle1 \) and \( \angle2 \) are supplementary angles (\( \angle1+\angle2 = 180^{\circ} \))
\( m\angle2=180^{\circ}-m\angle1 \)
Substitute \( m\angle1 = 98^{\circ} \)
\( m\angle2=180^{\circ}-98^{\circ}=82^{\circ} \)

Step3: Find \( m\angle3 \)

\( \angle2 \) and \( \angle3 \) are vertical angles.
So \( m\angle3 = m\angle2 = 82^{\circ} \)

Answer:

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