Question

two parallel lines are cut by a transversal as shown below. suppose m∠7 = 46°. find m∠2 and m∠4.

Explanation:

Step1: Identify vertical - angle relationship

$\angle7$ and $\angle5$ are vertical angles, so $m\angle5 = m\angle7=46^{\circ}$.

Step2: Use corresponding - angle relationship

$\angle2$ and $\angle5$ are corresponding angles. Since the two lines are parallel, $m\angle2 = m\angle5 = 46^{\circ}$.

Step3: Use linear - pair relationship

$\angle4$ and $\angle2$ are a linear - pair. So $m\angle4=180^{\circ}-m\angle2$. Substituting $m\angle2 = 46^{\circ}$, we get $m\angle4 = 180 - 46=134^{\circ}$.

Answer:

$m\angle2 = 46^{\circ}$
$m\angle4 = 134^{\circ}$