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.
