Droplet impact on biphilic surfaces with a wettability contrast has been intensively studied in recent years. In this work the effects of tilting and apex angles on droplet transport dynamics after impacting on a wedge-patterned biphilic surface at low Weber numbers were investigated experimentally. The biphilic surface was fabricated by applying a hydrophobic polymer coating on a bare silicon surface. According to the experimental results, a larger apex angle below 67.4 degrees can accelerate the droplet effectively at first. Then the friction force controls the droplet movement and reduces the speed. The tilting angle along the hydrophilic direction activates the droplet. If the gravity component is opposite to the hydrophilic direction and the tilting angle is over 15 degrees, the droplet can hardly move toward the hydrophilic area. By modeling the hydrodynamics of the droplet movement after impact on a biphilic surface with assumptions of no evaporation, no Marangoni effect, negligible dynamic contact angle variation and negligible rotation effect, the surface tension values versus the position at different apex angles are derived. The predicted position versus time trends agree well with the experimental data. This study aims to provide a better understanding of the mechanisms of droplet hydrodynamics on wedge-patterned biphilic surfaces at low Weber numbers.