It looks like this is from Princeton review, right?
Actually C is trap answer here.
Actually the opposite angles of equal sides of a triangle are equal.(mind it of a Single triangle)
Here in the first case two sides are equal but that are from different triangle(AD from ADB triangle, DC from BDC triangle); so that formula will not work here.
For the second case, both sides are from a single triangle. So, the formula works here!!!!!!!