Question

part 5 of 7
in the figure, m is parallel to n and m∠4 = 122°. find the measures of the other angles.
m∠6 = 122°
m∠2 = 122°
m∠8 = 122°
m∠5 = 58°
m∠3 = □°

Explanation:

Step1: Vertical angles

Vertical angles are equal. Since \(m\angle4 = 122^{\circ}\), and \(\angle4\) and \(\angle6\) are vertical angles, \(m\angle6=122^{\circ}\). \(\angle2\) and \(\angle8\) are also vertical angles with \(\angle4\), so \(m\angle2 = 122^{\circ}\), \(m\angle8=122^{\circ}\).

Step2: Linear - pair relationship

\(\angle4\) and \(\angle5\) form a linear pair (\(\angle4+\angle5 = 180^{\circ}\)). Given \(m\angle4 = 122^{\circ}\), then \(m\angle5=180 - 122=58^{\circ}\).

Step3: Vertical - angles and linear - pair for \(\angle3\)

\(\angle3\) and \(\angle5\) are vertical angles. Since \(m\angle5 = 58^{\circ}\), then \(m\angle3=58^{\circ}\).

Answer:

\(m\angle6 = 122^{\circ}\), \(m\angle2 = 122^{\circ}\), \(m\angle8 = 122^{\circ}\), \(m\angle5 = 58^{\circ}\), \(m\angle3 = 58^{\circ}\)