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Let BAC  = 47°

Note that angles ABO and ACO each  = 90°

So....the quadrilatral formed by ABOC  has interior angles that will sum to 360°

And  we  know three of the angles and we are trying to find angle BOC

So

47 + 90 + 90 + BOC  = 360    .......simplify

227 + BOC  = 360      subtract 227 from both sides

BOC  = 133

And since this is a central angle, it has the same measure as the arc we are interested in, namely, minor arc BC......so....the measure of the arc intercepted by the tangents = 133°