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.
m ∠2=m ∠3
We already know that m ∠2= 40, so m ∠3= 40 as well. By the definition of a rectangle, we know that ABCD has four right angles. Therefore, the measure of m ∠BCD is 90.
m ∠BCD= 90
With the Angle Addition Postulate we can express m ∠BCD as a sum of m ∠3 and m ∠4.
m ∠3 + m ∠4 = m ∠BCD
⇕
m ∠3 + m ∠4 = 90
We know that m ∠3= 40. We will substitute it into the equation above to find the measure of ∠4.
40 + m ∠4 = 90
Let's solve it!
Because our quadrilateral is a rectangle, its diagonals are congruent and bisect each other. Therefore, the triangle formed by ∠4, ∠5, and ∠6 is an isosceles triangle, and by the definition of an isosceles triangle, the measures of ∠6 and ∠4 are equal.
m ∠6 = m ∠4
⇕
m ∠6 = 50
