If parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent.
Therefore, ∠ 1 and ∠ 5 are congruent. Since the measure of ∠ 1 is given, we can use it.
m ∠ 5=m ∠ 1 ⇔ m ∠ 5 = 30
By the definition of a rectangle, we know that WXYZ has four right angles. Therefore, the measure of m ∠ WYZ is 90.
m ∠ WYZ= 90
With the Angle Addition Postulate we can express m ∠ WYZ as a sum of m ∠ 5 and m ∠ 6.
m ∠ 5 + m ∠ 6 = m ∠ WYZ
⇕
m ∠ 5 + m ∠ 6 = 90
We already know that m ∠ 5= 30. We will substitute this value into our equation and solve for m∠ 6.
