Answer:
m∠U = 104°
Explanation:
If in triangle UVW, UV ≅ WU, then ΔUVW is an isosceles triangle.
The congruent base angles are ∠V and ∠W, so m∠V = m∠W.
Interior angles of a triangle sum to 180°:
⇒ m∠U + m∠V + m∠W = 180°
Given m∠W = 38°:
⇒ m∠U + 38° + 38° = 180°
⇒ m∠U + 76° = 180°
⇒ m∠U = 104°