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We have designed a new filter pack array to measure angular variations in x-ray spectra during a single shot. The filter pack was composed of repeating identical columns of aluminum and copper filters of varying thicknesses. These columns were located at different positions to measure the spectrum at each corresponding angle. This array was utilized in an experiment to measure the energy evolution of betatron x rays in a laser wakefield accelerator by curving the wakefield with a transverse density gradient, streaking the x rays across the array in front of an x-ray charge-coupled device (CCD) camera. After subtracting the background and “flattening” the image to remove spatial nonuniformities, a critical energy was calculated for each position that produced the best agreement with the measured signal. There was a clear change in critical energy with angle, shedding light on the dynamics of the electrons that traveled through the accelerator. These angles correspond to distinct emission times, covering a timescale of tens of picoseconds. The filter pack was capable of recovering these angular details without the impact of errors introduced by shot-to-shot variability.