Question

in the figure below, m∠4 = 127°. find m∠1, m∠2, and m∠3.

Explanation:

Step1: Identify vertical - angle relationship

Vertical angles are equal. $\angle1$ and $\angle4$ are vertical angles.
So $m\angle1=m\angle4 = 127^{\circ}$

Step2: Identify supplementary - angle relationship

$\angle1$ and $\angle2$ are supplementary angles (a linear pair), so $m\angle1 + m\angle2=180^{\circ}$. Then $m\angle2=180^{\circ}-m\angle1$. Substituting $m\angle1 = 127^{\circ}$, we get $m\angle2=180 - 127=53^{\circ}$

Step3: Identify vertical - angle relationship again

$\angle2$ and $\angle3$ are vertical angles. So $m\angle3=m\angle2 = 53^{\circ}$

Answer:

$m\angle1 = 127^{\circ}$
$m\angle2 = 53^{\circ}$
$m\angle3 = 53^{\circ}$