180^{0}=m\left(\widehat{ADB}\right)+m\left(\widehat{BDC}\right)\Rightarrow 180^{0}=102^{0}+m\left(\widehat{BDC}\right)\Rightarrow 180^{0}-108^{0}=m\left(\widehat{BDC}\right)\Rightarrow m\left(\widehat{BDC}\right)=72^{0}