The Mojette transform is an exact discrete version of the Radon transform that can be exactly implemented from the discrete object with its associated geometry. This exact method requires a very large set of projections that will not be acquired. Then, the goal of this paper is to show how the Mojette projections set can be interpolated to enlarge the set of projections. The second part of the paper is devoted to recall the sampling geometry both of the reconstructed image and the projections. The third part of the paper presents two Mojette reconstruction algorithms: an exact backprojection filtering Mojette scheme which needs a (large) finite number of projections and its equivalent FBP-Mojette method. The fourth section presents an angular interpolation method used to generate a suitable set of projections from the known information. The reconstruction results given by this new set of angles used with the two reconstruction methods presented are given and discussed. The quality assessement of the reconstruction algoritms in the case of an insufficient number of projections is done using synthetic phantoms.