Question

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

Explanation:

Step1: Identify angle - relationship

Given that when two parallel lines are cut by a transversal, corresponding angles are congruent. $\angle2$ and $\angle6$ are corresponding angles, and $\angle6$ and $\angle5$ are vertical - angles. Also, $\angle2$ and $\angle8$ are alternate exterior angles.

Step2: Use vertical - angle property

Since vertical angles are congruent, and $\angle6$ and $\angle5$ are vertical angles. Also, $\angle2$ and $\angle6$ are corresponding angles, so $m\angle5=m\angle6 = m\angle2$. Given $m\angle2 = 42^{\circ}$, then $m\angle5=42^{\circ}$.

Step3: Use alternate - exterior - angle property

When two parallel lines are cut by a transversal, alternate exterior angles are congruent. $\angle2$ and $\angle8$ are alternate exterior angles. So $m\angle8=m\angle2 = 42^{\circ}$.

Answer:

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