Question

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 = □°

Explanation:

Step1: Vertical angles

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

Step2: Corresponding angles

When two parallel lines \(m\) and \(n\) are cut by a transversal, corresponding angles are equal. \(\angle4\) and \(\angle2\) are corresponding angles, so \(m\angle2 = 122^{\circ}\).

Step3: Vertical angles

\(\angle2\) and \(\angle8\) are vertical angles. So \(m\angle8=122^{\circ}\).

Step4: Linear - pair relationship

\(\angle4\) and \(\angle5\) form a linear pair. The sum of angles in a linear pair is \(180^{\circ}\). So \(m\angle5=180^{\circ}-m\angle4\). Substitute \(m\angle4 = 122^{\circ}\), then \(m\angle5=180 - 122=58^{\circ}\).

Answer:

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