The Energy hole problem, a common phenomenon in wireless sensor networks, significantly decreases the lifetime of any deployed network. Some of the popular techniques to minimize such problems are using mobile sinks instead of static sinks, extending the transmission range dynamically, and deploying redundant sensor nodes near the base station/sink. The major drawback to these techniques are that energy holes may still be created at some point due to their static nature of deployment, despite having the overall residual energy very high. In this research work, we adopt a new approach by dividing the whole network into equiangular wedges and merging a wedge with its neighboring wedge dynamically whenever individual residual energy of all member nodes of a wedge fall below a threshold value. We also propose an efficient Head Node (HN) selection scheme to reduce the transmission energy needed for forwarding data packets among Head Nodes. Simulation results show that WEMER, our proposed WEdge MERging based scheme, provides significantly higher lifetime and better energy efficiency compared to state-of-the-art Power-Efficient Gathering in Sensor Information Systems (PEGASIS) and contemporary Concentric Clustering Scheme (CCS), and Multilayer Cluster Designing Algorithm (MCDA).