in the diagram below, B, C and D are all on the same line, angle BAC = 24 degrees, and AB= AC = CD .

No image is shown, sageatron.....  

OK....!!!

Note that since AB  = AC....then angles ABC  and ACB  are  equal.....

So ACB  =  (180 - 24) / 2  =   156 / 2  =  78°

And ACD  is supplemental to ACB...so ACD  = 180 - 78  =  102°

And since AC  = CD....then angles ADC  and CAD are equal

So.... ADC  =  (180 - 102) / 2  =  78/2   =  39°  =  "x"