Find the missing angle in the triangle below if the sum of two sides is given

Question

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 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. 😀

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 it vertices being either on $\overline{AD}$ or $\overline{AB}$ because we have to use the given sum). That's one way to potentially solve it, I think? This is probably not so tough, but I just despise geometry. :sob:

Answer 1

Hint:

Determine $\angle DAE=\angle DEA$ and find two pairs of congruent triangles