Question

the parallel lines are intersected by a transversal. find m∠4 and m∠7 if m∠2 = 55

Explanation:

Step1: Use vertical - angle property

Vertical angles are congruent. $\angle2$ and $\angle4$ are vertical angles. So $m\angle4=m\angle2$. Since $m\angle2 = 55$, then $m\angle4=55$.

Step2: Use alternate - exterior angles property

$\angle2$ and $\angle7$ are alternate - exterior angles. When two parallel lines are cut by a transversal, alternate - exterior angles are congruent. So $m\angle7=m\angle2$. Since $m\angle2 = 55$, then $m\angle7 = 55$.

Answer:

$m\angle4 = 55$, $m\angle7=55$