Question

m∠1 = m∠2 =

Explanation:

Step1: Identify angle - type relationship

The 122 - degree angle and ∠1 are vertical angles.

Step2: Apply vertical - angle property

Vertical angles are equal, so $m\angle1 = 122^{\circ}$.

Step3: Identify supplementary - angle relationship

∠1 and ∠2 are supplementary angles (linear pair), so $m\angle1+m\angle2 = 180^{\circ}$.

Step4: Calculate $m\angle2$

$m\angle2=180^{\circ}-m\angle1 = 180 - 122=58^{\circ}$.

Answer:

$m\angle1 = 122^{\circ}$, $m\angle2 = 58^{\circ}$