The nature of the magnetic transition of the half-filled triangular antiferromagnet Ag2NiO2 with T-N=56 K was studied with positive muon-spin-rotation and relaxation (mu+SR) spectroscopy. Zero field mu+SR measurements indicate the existence of a static internal magnetic field at temperatures below T-N. Two components with slightly different precession frequencies and wide internal-field distributions suggest the formation of an incommensurate antiferromagnetic order below 56 K. This implies that the antiferromagnetic interaction is predominant in the NiO2 plane in contrast to the case of the related compound NaNiO2. An additional transition was found at similar to 22 K by both mu+SR and susceptibility measurements. It was also clarified that the transition at similar to 260 K observed in the susceptibility of Ag2NiO2 is induced by a purely structural transition.