Question

finding angle measures given two parallel lines cut by a transversal. two parallel lines are cut by a transversal as shown below. suppose m∠5 = 129°. find m∠2 and m∠3.

Explanation:

Step1: Identify vertical - angle relationship

$\angle5$ and $\angle7$ are vertical angles. Vertical angles are equal. So $m\angle7 = m\angle5=129^{\circ}$.

Step2: Identify corresponding - angle relationship

$\angle2$ and $\angle7$ are corresponding angles. For parallel lines cut by a transversal, corresponding angles are equal. So $m\angle2 = m\angle7 = 129^{\circ}$.

Step3: Identify supplementary - angle relationship

$\angle3$ and $\angle2$ are supplementary angles (linear - pair). Since the sum of angles in a linear - pair is $180^{\circ}$, we have $m\angle3=180^{\circ}-m\angle2$. Substituting $m\angle2 = 129^{\circ}$, we get $m\angle3 = 180 - 129=51^{\circ}$.

Answer:

$m\angle2 = 129^{\circ}$
$m\angle3 = 51^{\circ}$