Question

two parallel lines are cut by a transversal as shown below. suppose m∠3 = 82°. find m∠5 and m∠8.

Explanation:

Step1: Identify angle - angle relationships

$\angle3$ 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 $\angle3$ and $\angle5$ are alternate - interior angles and $m\angle3 = 82^{\circ}$, then $m\angle5=82^{\circ}$.

Step3: Identify another angle - angle relationship

$\angle3$ and $\angle8$ are corresponding angles. When two parallel lines are cut by a transversal, corresponding angles are congruent.

Step4: Find $m\angle8$

Since $\angle3$ and $\angle8$ are corresponding angles and $m\angle3 = 82^{\circ}$, then $m\angle8 = 82^{\circ}$.

Answer:

$m\angle5 = 82^{\circ}$
$m\angle8 = 82^{\circ}$