Angiogenesis is a crucial process that leads to the formation of new blood vessels from an existing vasculature, ensuring the supply of nutrients and oxygen to tissues while facilitating the removal of metabolic waste. We propose a comprehensive mathematical framework for simulating tumor-induced angiogenesis, integrating the growth of an arbitrarily complex vascular network with fluid flow and oxygen transport in both tissue and vessels, and the dispersion of an angiogenic growth factor (VEGF) within the tissue. The model equations for the three unknowns (namely fluid pressure, oxygen concentration and VEGF concentration) are first defined inside the tissue and within the vessels, represented as cylindrical connected tubes. This initial 3D-3D problem is then reformulated into a corresponding 3D-1D approximation by reducing the cylindrical vessels to their centerlines and simultaneously extending the outer domain to fill the voids. The evolving geometry of the vascular network is captured using a discrete tip-tracking model, which monitors the positions of capillary tips over time, defining a hybrid approach that couples a continuous representation of fluid and chemicals with a discrete model for capillary evolution. To solve the resulting problem, we employ a numerical scheme based on a PDE constrained domain decomposition strategy that allows to write the 3D and the 1D problem on non conforming meshes and to solve them independently. This coupling strategy ensures robust and flexible handling of the evolving vascular network without the need for remeshing as the network grows, maintaining computational feasibility even for complex geometries. Numerical simulations performed under varying tissue conditions demonstrate how capillary sprouting, network formation and tumour growth depend on the spatial distributions of VEGF and oxygen. These results elucidate the complex interplay between oxygen transport and angiogenic signaling, providing quantitative insights into the mechanisms driving tumor vascularization and potential therapeutic targets.