Direct current slice velocity map ion images of the HCl(nu' = 0, J') products from the photoinitiated reactions of ground state Cl atoms with ethane, oxirane (c-C2H4O), and oxetane (c-C3H6O), at respective mean collision energies of 5.5, 6.5, and 7.3 kcal mol-1(-1), were analyzed using a Legendre moment fitting procedure. The experimental method and the fitting technique were tested by comparing the derived center-of-mass (CM) frame angular scattering distribution for the HCl(v' = 0, J' = 1) products from the reaction of Cl + C2H6 with those determined by Suits and co-workers from a crossed molecular beam experiment. For the Cl + c-C2H4O reaction, a broad, forward, and backward peaking CM frame angular distribution of HCl(nu' = 0, J' = 2) products was determined, with an average fraction of the available energy released as product translational energy of f t, equal to 0.52 +/- 0.18. The HCl consumes only 1% of the available energy, and conservation arguments dictate that the radical coproduct is significantly internally excited, corresponding to an average fraction of the available energy of f int(c-C2H3O), equal to 0.47 +/- 0.18. For the reaction of oxetane with Cl atoms, abstraction of H atoms is possible from carbon atoms from positions either alpha or beta to the O atom. The contributions to the reaction from these two H-atom abstraction channels were estimated to be 63 and 37%, consistent with an unbiased propensity for removal of alpha- and beta-H atoms that are present in 2:1 abundance. The angular scatter of products in the CM frame is also broad and forward-backward peaking and is reminiscent of the products of the Cl + CH3OH and CH3OCH3 reactions. The derived mean fraction of the available energy channelled into product translation is f t = 0.54 +/- 0.12 for each of the two abstraction pathways. With only a small amount of energy in the rotation of the HCl(nu' = 0), the remainder is accounted for by excitation of the radical coproduct internal modes, with f int(c-C3H5O) = 0.42 +/- 0.12 for both alpha- and beta-H abstraction. The broad product scattering in the CM frame observed for both reactions of Cl atoms with the cyclic ethers is consistent with reactive collisions over a wide range of impact parameters, as might be expected for barrierless reactions with loose transition states.