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The global stabilization of planar angle rigid formations is shown to be a challenging problem in the existing literature even when relative position measurements are available among neighboring agents. Inspired by an angle-induced linear constraint existing in each triangle, this paper proposes efficient formation control laws to achieve the global stabilization of triangularly angle rigid formations using local relative position measurements. Compared to some other globally stable formation control systems using local relative position measurements, our approach is shown to be more computationally effective and scalable. Moreover, by additionally controlling the relative position between a pair of neighboring agents, we propose two modified formation control laws to globally stabilize triangularly angle rigid formation with prescribed orientation and scale. Compared to other formation stabilization approaches with prescribed orientation and scale, the proposed formation control law can guarantee global stability instead of almost global stability.