Question

in the figure below, ( mangle2 = 99^{circ} ). find ( mangle1 ), ( mangle3 ), and ( mangle4 ).

Explanation:

Step1: Use the property of adjacent angles (supplementary angles)

Adjacent angles on a straight line sum to \(180^{\circ}\). Given \(m\angle2 = 99^{\circ}\), and \(\angle1\) and \(\angle2\) are adjacent angles. So \(m\angle1=180^{\circ}-m\angle2\).

$$m\angle1 = 180^{\circ}-99^{\circ}=81^{\circ}$$

Step2: Use the property of vertical angles

Vertical angles are equal. \(\angle1\) and \(\angle3\) are vertical angles, so \(m\angle3=m\angle1\).

$$m\angle3 = 81^{\circ}$$

Step3: Use the property of vertical angles

\(\angle2\) and \(\angle4\) are vertical angles. So \(m\angle4=m\angle2\).

$$m\angle4 = 99^{\circ}$$

Answer:

\(m\angle1 = 81^{\circ}\), \(m\angle3 = 81^{\circ}\), \(m\angle4 = 99^{\circ}\)