Question

two parallel lines are cut by a transversal as shown below. suppose m∠8 = 39°. find m∠1 and m∠3.

Explanation:

Step1: Identify vertical - angle relationship

$\angle8$ and $\angle6$ are vertical angles. Since vertical angles are congruent, $m\angle6=m\angle8 = 39^{\circ}$.

Step2: Identify corresponding - angle relationship

$\angle1$ and $\angle5$ are corresponding angles, and $\angle5$ and $\angle6$ are a linear - pair. $\angle1$ and $\angle6$ are also corresponding angles. So $m\angle1 = 39^{\circ}$.

Step3: Identify supplementary - angle relationship

$\angle3$ and $\angle6$ are same - side interior angles. Since the two lines are parallel, same - side interior angles are supplementary. So $m\angle3=180^{\circ}-m\angle6$.
$m\angle3 = 180 - 39=141^{\circ}$

Answer:

$m\angle1 = 39^{\circ}$
$m\angle3 = 141^{\circ}$