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 corresponding - angles

$\angle5$ and $\angle1$ are corresponding angles. Since the two lines are parallel, $m\angle1 = m\angle5=148^{\circ}$.

Step2: Find $m\angle2$

$\angle1$ and $\angle2$ are supplementary angles (linear - pair). So $m\angle2 = 180^{\circ}-m\angle1$. Substituting $m\angle1 = 148^{\circ}$, we get $m\angle2=180 - 148=32^{\circ}$.

Step3: Find $m\angle4$

$\angle1$ and $\angle4$ are vertical angles. Vertical angles are equal. So $m\angle4 = m\angle1 = 148^{\circ}$.

Answer:

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