We know that in a triangle, the sum of the interior angles is 180 degrees.
So,
m∠T + m∠U + m∠V = 180.
Substituting the given values,
(7x+10) + (x+2) + (3x+3) = 180.
11x + 15 = 180.
Simplifying the equation,
11x = 165,
x = 15.
Now we can substitute the value of x back into the equation for m∠U,
m∠U = (x+2) = 15 + 2 = 17.
Therefore, m∠U is 17 degrees.