Lines AB and CD are perpendicular to each other. If 1 measures (4x + 4)°, and 2 measures 10°, what is the value of x?

Since AB and CD are perpendicular, angles 1 and 2 are complementary, which means they add up to 90 degrees.

Therefore, we have the equation (4x + 4)° + 10° = 90°.
Combining like terms, we get 4x + 14 = 90.
Subtracting 14 from both sides of the equation, we obtain 4x = 76.
Dividing both sides by 4, we find x = <<19=19>>19. Answer: \boxed{19}.