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Note, angle BOC is supplementary to angle AOB

So   AOB + BOC  = 180

So

67 + BOC  = 180

BOC  = 113

And angle BAC is an inscribed angle which intercepts the same arc as central angle BOC.......and an inscribed angle which intercepts the same arc as a central angle measures (1/2) of the central angle

So.....BAC  = (1/2)(BOC)   =  56.5° 

113