Hey Gurram,

Unfortunately, Jim has misunderstood this question. This is entirely realistic, and does not require any knowledge of trigonometry to solve. It's hard for me to explain without lots of pictures, which would take forever, but I'm going to do my best!

1) If AD = DC, then Angle ACD = Angle DAC. (Rule: Equal sides are opposite equal angles.)

2) We know that Angle ACD = 40. That means that angle DAC is also 40.

3) Because a line is made up of 180 degrees, Angle ACB must be 140.

4) At this point, we can eliminate answer choices D and E, because the other angles must be less than 40 degrees.

5) The question tells us that AC = BD. This means that BC < AC. If that's the case, the angle opposite AC (ABC) must be greater than the angle opposite BC (BAC).

6) The answer can't be 20, because then the two remaining angles would BOTH be 20. It can't be 30, because then BAC would be bigger than ABC. The answer must be 10 degrees.

Let me know if that makes sense. If not, I can attempt to put up a bunch of pictures! : )

-t