Question

two parallel lines are cut by a transversal as shown below. suppose m∠7 = 101°. find m∠2 and m∠4.

Explanation:

Step1: Identify vertical - angle relationship

$\angle 7$ and $\angle 5$ are vertical angles. Since vertical angles are congruent, $m\angle 5=m\angle 7 = 101^{\circ}$.

Step2: Identify corresponding - angle relationship

$\angle 5$ and $\angle 1$ are corresponding angles. For parallel lines cut by a transversal, corresponding angles are congruent. So $m\angle 1=m\angle 5 = 101^{\circ}$.

Step3: Identify linear - pair relationship for $\angle 2$

$\angle 1$ and $\angle 2$ form a linear pair. A linear - pair of angles is supplementary, so $m\angle 1 + m\angle 2=180^{\circ}$. Then $m\angle 2=180 - m\angle 1=180 - 101=79^{\circ}$.

Step4: Identify alternate - interior - angle relationship for $\angle 4$

$\angle 4$ and $\angle 5$ are alternate - interior angles. For parallel lines cut by a transversal, alternate - interior angles are congruent. So $m\angle 4=m\angle 5 = 101^{\circ}$.

Answer:

$m\angle 2 = 79^{\circ}$
$m\angle 4 = 101^{\circ}$