Question

two parallel lines are cut by a transversal as shown below. suppose ( mangle3 = 39^{circ}). find ( mangle5) and ( mangle8).

Explanation:

Step1: Find $m\angle5$

$\angle3$ and $\angle5$ are alternate interior angles.
Since alternate interior angles are congruent when two parallel lines are cut by a transversal, $m\angle5=m\angle3 = 39^{\circ}$.

Step2: Find $m\angle8$

$\angle5$ and $\angle8$ are vertical angles.
Since vertical angles are congruent, $m\angle8=m\angle5 = 39^{\circ}$.

Answer:

$m\angle5 = 39^{\circ}$
$m\angle8 = 39^{\circ}$