Question

the parallel lines are intersected by a transversal. find m∠3 and m∠1 if m∠2 = 55

Explanation:

Step1: Identify angle - pair relationship for ∠2 and ∠3

∠2 and ∠3 are vertical angles. Vertical angles are congruent.
$m\angle2 = m\angle3$

Step2: Substitute the value of ∠2

Given $m\angle2=55^{\circ}$, so $m\angle3 = 55^{\circ}$

Step3: Identify angle - pair relationship for ∠1 and ∠2

∠1 and ∠2 are a linear - pair. A linear - pair of angles is supplementary, meaning $m\angle1 + m\angle2=180^{\circ}$

Step4: Solve for ∠1

$m\angle1=180^{\circ}-m\angle2$. Substitute $m\angle2 = 55^{\circ}$, then $m\angle1=180 - 55=125^{\circ}$

Answer:

$m\angle3 = 55^{\circ}$, $m\angle1 = 125^{\circ}$