If parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent.
Therefore, ∠2 and ∠3 are congruent and their measures are equal. Since the measure of ∠2 is given, we can use it.
m ∠3=m ∠2 ↔ m ∠3 = 40
Because our quadrilateral is a rectangle, its diagonals are congruent and bisect each other. Therefore, the triangle formed by ∠3, ∠7, and ∠8 is an isosceles triangle, and because of the definition of an isosceles triangle, m ∠7 and m ∠3 are congruent.
m ∠7=m ∠3 ↔ m ∠7 = 40
Recall the Interior Angles Theorem.
Using that, we can write an equation for the angles of the triangle.
m ∠3 + m ∠7 + m ∠8 = 180
⇕
40 + 40 + m ∠8 = 180
Finally, let's solve it to find m ∠8.
