What is the value of x?
x =___

According the Vertical Angles Theorem, the angles are congruent.
Set up your equation : 4x + 7 = 5(x - 4)
Distribute in the second equation : 4x + 7 = 5x - 20
Subtract 4x from both sides : 7 = x - 20
Add 20 to both sides : 27 = x
x = 27