Final answer:
A nurse's use of a back massage to relieve pain is based on the Gate Control Theory, which posits that such non-painful input can inhibit the perception of pain.
Step-by-step explanation:
The theory that motivates the intervention of a back massage to relieve pain is the Gate Control Theory. This theory suggests that non-painful input, such as the tactile sensation from a massage, can close the 'gates' to painful input, which prevents pain sensation from traveling to the central nervous system. Therefore, the correct answer to this question is A) Gate Control Theory.