We utilise minimum-norm least-squares based on the indirect observations methods to adjust our 2-dimensional triangulation network. The main objective of this paper is to optimally adjust the approximate coordinates of the nodes (points) of the given network. The network observations (11 measured distances and 17 angles) have been adjusted by being combined in linear system of equations in terms of free-network adjustment procedure to rigorously adjust the approximate coordinates over the network points. We obtained better converged values by applying an iterative procedure, the minimum corrections for the free-network coordinates are obtained after a number of five iterations. The data snooping procedure has been used to test the reliability and precision of the network observations. The T-Test criterion is then applied for gross error detection, five angles and two lines are suspected to include gross errors at a critical value of 1.98.
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