\widehat{BID} = 360^o - \widehat{IBD} - \widehat{IDC} - \widehat{C} = 360^o - \dfrac{1}{2}(\widehat{B} + \widehat{D}) - \widehat{C} = 360^o - \dfrac{1}{2}(360^o - \widehat{A} - \widehat{C}) - \widehat{C} = 180^o+\dfrac{1}{2}(\widehat{A} - \widehat{C} ) = 180^o + \dfrac{1}{2}.60^o = 210^o
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