Question

Given that: mACD= (12.x+ 15) mBCE=(20x- 9) Find mLDCE in degrees.

Answer 1

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:

`\begin{gathered} \text{mACD}=\text{mBCE} \\ 12x+15=20x-9 \\ 15+9=20x-12x \\ 24=8x \\ x=(24)/(8) \\ x=3 \end{gathered}`

Then we can write the equation for DCE as:

`\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}`

The measure of DCE is 129 degrees.