From the second and third steps, we know that m∠TUV = m∠1 + m∠2. We also know that m∠XWV = m∠3 + m∠4. Since ∠TUV and ∠XMV both measure 90°, we can set their measures equal to each other:
m∠TUV = m∠XMV
or equivalently:
m∠1 + m∠2 = m∠3 + m∠4
Next, we can use the fact that ∠1 ≅ ∠3 to say that m∠1 = m∠3, while allows us to replace one with the other. Here, we'll replace m∠3 with m∠1:
m∠1 + m∠2 = m∠1 + m∠4
Subtracting m∠1 from either side:
m∠2 = m∠4, which implies that ∠2 ≅ ∠4, as we wanted to show.