Answer:
[tex]\huge\boxed{\sf <WVT = 40\°}[/tex]
Step-by-step explanation:
According to one of the tangent-secant theorems,
∠WVT = [tex]\frac{1}{2} (arc\ TW-arc\ UW)[/tex]
Given that:
∠WVT = (3x + 4)°
arc TW = (14x + 7)°
arc UW = (7x + 11)°
Solution:
3x + 4 = 1/2 (14x + 7 - (7x + 11))
3x + 4 = 1/2 (14x + 7 - 7x - 11)
3x + 4 = 1/2 ( 7x - 4 )
Multiply both sides by 2
2 ( 3x + 4 ) = 7x - 4
6x + 8 = 7x - 4
Combining like terms
7x - 6x = 8 + 4
x = 12
Finding ∠WVT:
∠WVT = (3x + 4)°
∠WVT = (3(12)+4)°
∠WVT = (36+4)°
∠WVT = 40°
[tex]\rule[225]{225}{2}[/tex]
Hope this helped!
~AH1807
Peace!
