We will start by drawing the lines and angles:
By the properties of the angles that are opposed by the vertex, we know that the measure of the angle AEC and the measure of the angle DEB are the same.
So we can express:
[tex]\begin{gathered} m\text{AEC}=m\text{DEB} \\ 12x+5=x+49 \\ 12x-x=49-5 \\ 11x=44 \\ x=\frac{44}{11} \\ x=4 \end{gathered}[/tex]So we can calculate DEB as:
[tex]\text{DEB}=x+49=4+49=53[/tex]The angle DEB has a measure of 53 degrees.
