The required proof is stated in the explanation below.
Two or more triangles are said to be congruent if the corresponding sides and internal angles have equal measures. Thus triangles WXV and YXZ are congruent, as such we can proof that;
Statements Reasons
1. WX = XY, VX = XZ Given
2. <WXV = <YXZ Vertical Angles Theorem
3. ΔVXW ≅ ΔYXZ Congruent Property
4. <WVX ≅ <YZX Alternate Angle Property