自己画图结合着我的解答看吧
∠A+∠B+∠C=180
∠D=180-∠B/2-∠BCD
180-∠B/2-(∠C+(180-∠C)/2)
=90-1/2(∠B+∠C)
=90-1/2(180-∠A)=∠A/2=a/2