<|im_start|>system
You are a helpful assistant. You first think about the reasoning process in the mind and then provide the user with the answer. You should try to truely solve the question by yourself without cheating.  <|im_end|>
<|im_start|>user
 
In trapezoid \( ABCD \) with \( AD \parallel BC \), \(\angle ABC = 108^\circ\) and \(\angle ADC = 54^\circ\). On the ray \( BA \) beyond point \( A \) there is a point \( K \) such that \( AK = BC \). Find \(\angle DKC \) if it is known that \(\angle BKC = 27^\circ\). Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>
<|im_start|>assistant
Let me solve this step by step.
<think>
user
18

In trapezoid \( ABCD \) with \( AD \parallel BC \), \(\angle ABC = 108^\circ\) and \(\angle ADC = 54^\circ\). On the ray \( BA \) beyond point \( A \) there is a point \( K \) such that \( AK = BC \). Find \(\angle DKC \) if it is known that \(\angle BKC = 27^\circ\).
test