Protein 3D structure prediction has advanced significantly in recent years due to improving contact prediction accuracy. This improvement has been largely due to deep learning approaches that predict inter-residue contacts and, more recently, distances using multiple sequence alignments (MSAs). In this work we present AttentiveDist, a novel approach that uses different MSAs generated with different E-values in a single model to increase the co-evolutionary information provided to the model. To determine the importance of each MSA's feature at the inter-residue level, we added an attention layer to the deep neural network. We show that combining four MSAs of different E-value cutoffs improved the model prediction performance as compared to single E-value MSA features. A further improvement was observed when an attention layer was used and even more when additional prediction tasks of bond angle predictions were added. The improvement of distance predictions were successfully transferred to achieve better protein tertiary structure modeling.