Question

two parallel lines are cut by a transversal as shown below. suppose m∠5 = 148°. find m∠2 and m∠4.

Explanation:

Step1: Identify angle - angle relationships

$\angle5$ and $\angle2$ are alternate exterior angles. When two parallel lines are cut by a transversal, alternate exterior angles are congruent.

Step2: Find $m\angle2$

Since $\angle5$ and $\angle2$ are alternate exterior angles, $m\angle2 = m\angle5=148^{\circ}$.

Step3: Identify another angle - angle relationship

$\angle5$ and $\angle4$ are same - side interior angles. When two parallel lines are cut by a transversal, same - side interior angles are supplementary, that is $m\angle5 + m\angle4=180^{\circ}$.

Step4: Find $m\angle4$

$m\angle4 = 180^{\circ}-m\angle5$. Substitute $m\angle5 = 148^{\circ}$, so $m\angle4=180 - 148=32^{\circ}$.

Answer:

$m\angle2 = 148^{\circ}$
$m\angle4 = 32^{\circ}$