What is the reason for this geometric answer? 
$$\frac{AB}{CD} = \frac{2}{2.6} = 0.77\ldots$$
$$\frac{AC}{AD} = \frac{2}{2.6} = 0.77\ldots$$
$$\frac{BC}{AC} = \frac{2}{2.6} = 0.77\ldots$$
Therefore $\triangle ABC$ and $\triangle ACD$ are similar.
I know from the answer sheet that $y$ is $47^\circ$ and $x$ is $109^\circ$. I don't know the reasons why though. The diagram does not look like a parallelogram because both opposite sides are not parallel. 

Continuing,
since the triangles are similar,
$x = 109$
and
$y 
= CAD
=180-(109+47)
=180-156
=24
$.
