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X-ray pulses with peak energy of 0.6 Å have been generated via head-on collision of laser pulses from the high-field laser facility at Daresbury with the electron bunches of the ALICE energy recovery linear accelerator operating at 29.6 MeV. The angular distribution of the backscattered X-rays was obtained in single-shot using a scintillation screen. The temporal profile of the X-ray yield as a function of the time delay between the laser pulse and electron bunch was measured and agreed well with that expected from the collision point dependence of the laser-electron beam longitudinal overlap.