The new particle X recently discovered by the ATLAS and CMS Collaborations in searches for the Higgs boson has been observed to decay into , ZZ and WW , but its spin and parity, J P , remain a mystery, with J P = 0 + and 2 + being open possibilities. We use PYTHIA and Delphes to simulate an analysis of the angular distribution of gg! X! decays in a full 2012 data set, including realistic background levels. We show that this angular distribution should provide strong discrimination between the possibilities of spin zero and spin two with graviton-like couplings: 3 if a conservative symmetric interpretation of the log-likelihood ratio (LLR) test statistic is used, and 6 if a less conservative asymmetric interpretation is used. The WW and ZZ couplings of the Standard Model Higgs boson and of a 2 + particle with graviton-like couplings are both expected to exhibit custodial symmetry. We simulate the present ATLAS and CMS search strategies for X! WW using PYTHIA and Delphes, and show that their eciencies