已知AD=a+b，求解三角形中缺失的角度

I'm having a hard time solving this problem, so if anyone would be kind enough to point me in the right direction, I'd be forever grateful!

Find the value of the missing angle in the triangle below, if $AD=a+b$.

EDIT: Thanks for the tip! Duly noted! I'll be wary of this the next time, so please forgive me. :D

So, I can easily determine the following:
$$\angle ABC=40^\circ\wedge\angle DAC=100^\circ$$
Now, I'm not sure what to do next. I think maybe we'll have to do an auxiliary construction (another triangle with one of its vertices being either on $\overline{AD}$ or $\overline{AB}$ because we have to use the given sum). That's one way to potentially solve...

备注：内容来源于stack exchange，提问作者PinkBlack