So we already know that a triangle's angles sum up to 180 correct?
So what you want to do is use the given angle 114 to find Angle ACD.
What you do is do 180-114 and you get 66 which is the angles for ACB
and then you do \(66+66+66-x=180\)
\(\angle ACD = 48°\).
The answer is actually 18 Degrees since we have to find ACD, not DCB. Thanks for the answer though :)