Question

two parallel lines are cut by a transversal as shown below. suppose m∠8 = 64°. find m∠1 and m∠3.

Explanation:

Step1: Use vertical - angle property

$\angle8$ and $\angle5$ are vertical angles, so $m\angle5 = m\angle8=64^{\circ}$.

Step2: Use corresponding - angle property

$\angle1$ and $\angle5$ are corresponding angles, so $m\angle1 = m\angle5 = 64^{\circ}$.

Step3: Use linear - pair property

$\angle1$ and $\angle3$ are a linear pair. So $m\angle3=180 - m\angle1=180 - 64=116^{\circ}$.

Answer:

$m\angle1 = 64^{\circ}$, $m\angle3 = 116^{\circ}$