This letter proposes a novel resolution and power control scheme for energy-efficient mobile augmented reality (MAR) services through computation offloading to mobile edge computing (MEC). For this purpose, analytical models for the energy consumption of a MAR device (MD), detection accuracy of MAR objects, and service latency are rigorously formulated. Considering their tradeoff in MAR with MEC, a theoretical framework for the computation offloading problem of the MD that jointly optimizes the transmission power and frame resolution is designed. The proposed scheme significantly reduces energy consumption by 73.64 & x0025; with an accuracy loss of 1.6 & x0025; while guaranteeing the required latency constraint.