Question

parallel lines are cut by a transversal as shown below. if m∠2 = 42°. find m∠5 and m∠8.

Explanation:

Step1: Identify angle - pair relationship

$\angle2$ and $\angle5$ are alternate - interior angles. When two parallel lines are cut by a transversal, alternate - interior angles are congruent.

Step2: Find $m\angle5$

Since $\angle2 = 42^{\circ}$ and $\angle2\cong\angle5$, then $m\angle5 = 42^{\circ}$.

Step3: Identify angle - pair relationship for $\angle8$

$\angle2$ and $\angle8$ are corresponding angles. When two parallel lines are cut by a transversal, corresponding angles are congruent.

Step4: Find $m\angle8$

Since $\angle2 = 42^{\circ}$ and $\angle2\cong\angle8$, then $m\angle8 = 42^{\circ}$.

Answer:

$m\angle5 = 42^{\circ}$
$m\angle8 = 42^{\circ}$