Write a paragraph to prove that the measure of angle 4 is equal to the measure of angle 8

I think what you're talking about is proving that corresponding angles that are formed by a transversal intersecting two parallel lines.

Here is the proof:

Angle 4 and angle 6 are supplementary angles because they are adjacent angles formed by a line intersecting two parallel lines (parallelogram).

Angle 6 and angle 5 are supplementary angles since they lie in the same line and they have an adjacent side.

Angle 4 and angle 5 are congruent because of the two prior statements.

Angle 4 and angle 8 are congruent because they are vertical angles.

Angle 4 and angle 8 are congruent because of transitivity property (∠4 = ∠5, ∠5 = ∠8, so ∠4 = ∠8)