Some geometry

Problem:



In the figure CB and CD are opposite rays, CE bisects angle DCF and CG bisects FCB

Solution:

Because we have CE bisect angle DCF, therefore angle DCE = angle ECF, and so

$ \begin{eqnarray*} 4x + 15 &=& 6x -5 \\ 20 &=& 2x \\ x &=& 10 \end{eqnarray*} $

So angle DCE is $ 4x + 15 = 55 $.