Question

two parallel lines are cut by a transversal as shown below. suppose m∠5 = 132°. find m∠2 and m∠4.

Explanation:

Step1: Identify angle - relationship for ∠2 and ∠5

∠2 and ∠5 are alternate - interior angles. When two parallel lines are cut by a transversal, alternate - interior angles are congruent.
$m\angle2=m\angle5$

Step2: Substitute the value of ∠5

Since $m\angle5 = 132^{\circ}$, then $m\angle2=132^{\circ}$

Step3: Identify angle - relationship for ∠4 and ∠5

∠4 and ∠5 are same - side interior angles. When two parallel lines are cut by a transversal, same - side interior angles are supplementary, i.e., $m\angle4 + m\angle5=180^{\circ}$

Step4: Solve for ∠4

$m\angle4=180^{\circ}-m\angle5$
Substitute $m\angle5 = 132^{\circ}$, then $m\angle4=180 - 132=48^{\circ}$

Answer:

$m\angle2 = 132^{\circ}$
$m\angle4 = 48^{\circ}$