You have the measurements of angles TUV and TUW, these two angles share the vertex U and one side T, so we can assume they are adjacent:
Angle VUW has its vertex on U and its sides are W and V, this means that angles TUW and TUV are included in angle VUW.
According to the angle addition postulate you can determine that:
VUW= TUV + TUW
VUW= 35º+14º
VUW= 49º