Question

two parallel lines are cut by a transversal as shown below. suppose m∠2 = 51°. find m∠5 and m∠8.

Explanation:

Step1: Identify angle - relationships

$\angle2$ and $\angle5$ are alternate - interior angles. When two parallel lines are cut by a transversal, alternate - interior angles are congruent.
Since $m\angle2 = 51^{\circ}$, then $m\angle5=51^{\circ}$.

Step2: Identify another angle - relationship

$\angle2$ and $\angle8$ are corresponding angles. When two parallel lines are cut by a transversal, corresponding angles are congruent.
So $m\angle8 = 51^{\circ}$.

Answer:

$m\angle5 = 51^{\circ}$
$m\angle8 = 51^{\circ}$