The variety in fault geometry, fault interaction style, and evolution of the fault network above a weak planar preexisting fault as a result of a change in the strike angle (α) of the preexisting fault relative to the extension direction is investigated using three‐dimensional discrete element modeling. The preexisting fault shows three reactivation modes: (i) full reactivation (α ≥ 60°), (ii) partial reactivation (α = 45°), and (iii) little or no reactivation (α = 30°). A fully reactivated fault decreases the density, affects the orientation, and enhances the length and displacement of adjacent new faults. A partially reactivated fault generates some isolated fault segments along strike and also influences fault orientation. However, when the preexisting fault is not reactivated, its presence has little effect on the growth of new faults. Our study confirms that the reactivation pattern of a preexisting fault and its influence on new fault growth varies with its strike angle relative to the extension direction. It also demonstrates how a preexisting fault influences adjacent fault geometry and the fault network by changing the density, orientation, length, and displacement of newly formed faults. The work impacts understanding three‐dimensional fault geometries, the distribution, and evolution of fault networks in rift basins affected by preexisting faults and on predicting the extension direction of renewed rifting.