Answer
m$\angle$V=42$^{\circ}$
Work Step by Step
If $\overline{VT}$ is congruent to $\overline{VU}$ and m$\angle$T=69$^{\circ}$
then m$\angle$U will also be 69$^{\circ}$
Now, m$\angle$V+m$\angle$T+m$\angle$U=180$^{\circ}$
m$\angle$V+69$^{\circ}$+69$^{\circ}$=180$^{\circ}$
m$\angle$V=180$^{\circ}$-138$^{\circ}$
m$\angle$V=42$^{\circ}$
