ACD and BCE are vertical angles, so its measures are the same.
DCE is supplementary to ACD, so both angles add 180 degrees.
From the first sentence, we can write:
[tex]\begin{gathered} \text{mACD}=\text{mBCE} \\ 12x+15=20x-9 \\ 15+9=20x-12x \\ 24=8x \\ x=\frac{24}{8} \\ x=3 \end{gathered}[/tex]
Then we can write the equation for DCE as:
[tex]\begin{gathered} \text{mDCE}+\text{mACD}=180 \\ \text{mDCE}=180-\text{mACD} \\ \text{mDCE}=180-(12x+15) \\ \text{mDCE}=180-12\cdot3-15 \\ \text{mDCE}=180-36-15 \\ \text{mDCE}=129 \end{gathered}[/tex]
The measure of DCE is 129 degrees.
