Answer:
92°
Step-by-step explanation:
We know that [tex]\overline{QV}[/tex] is a straight line which means that we know that ∠QTU + ∠VTU = 180
11x+4+∠VTU = 180
∠VTU = 180-11x-4
∠VTU = 176-11x
Then, using the triangle inequality, we know that ∠VTU+∠TUV+∠UVT = 180
3x+14+54+176-11x=180
-8x+244=180
-8x = -64
x=8
Now we can substitute and solve for ∠UTQ
11(8)+4 = 88+4 = 92°
