A trig problem with two obtuse triangles

It was on a test I wrote, but I just wanna clarify if I did it correctly.

In the diagram,

http://img239.imageshack.us/img239/5135/trianglegj9.jpg

You're given:

In Triangle ACD,

Angle A, Angle C, and Side CD.

In Triangle ABD,

Angle B and Side AB

You're asked to find Angle A in Triangle ABD.

So, you start off by using the Law of Sines to obtain the value of AD in Triangle ACD.

Once you have that, you use Law of Sines again to obtain Angle D in Triangle ABD.

However, since that angle must be obtuse, you subtract your answer from 180 to obtain the real answer for Angle D.

Now, you just subtract that value and Angle B (given) from 180 to obtain Angle A.