If parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent.
Therefore, ∠ 2 and ∠ 3 are congruent. 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. By the definition of an isosceles triangle, we know that m ∠ 7 and m ∠ 3 are congruent.
m ∠ 7=m ∠ 3 ⇔ m ∠ 7 = 40
Therefore, the measure of ∠ 7 is 40.
