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

Corresponding angles are equal when parallel lines are cut by a transversal. $\angle2$ and $\angle5$ are corresponding angles. So $m\angle2 = m\angle5$. Since $m\angle5=148^{\circ}$, then $m\angle2 = 148^{\circ}$.

Step2: Identify supplementary - adjacent angles

$\angle5$ and $\angle8$ are a linear - pair, so $m\angle5 + m\angle8=180^{\circ}$. Also, $\angle4$ and $\angle8$ are corresponding angles. First, find $m\angle8 = 180^{\circ}-m\angle5=180 - 148=32^{\circ}$. Since $\angle4$ and $\angle8$ are corresponding angles, $m\angle4=m\angle8 = 32^{\circ}$.

Answer:

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