To solve for the angles $x$ and $y$, we'll use the Law of Sines.

Given:

• The side lengths are $18.7 \, \text{cm}$ and $15.2 \, \text{cm}$,
• The triangle is not a right triangle, so we will need more information.

First, let's find the third side, and check if we have sufficient information to proceed with either the Law of Sines or Cosines. I'll need to extract the angle information and process the problem.

Please allow me a moment.Upon further inspection of the image, I noticed that we do not have enough information in the diagram to directly compute the angles using the Law of Sines or Cosines, as we do not have a third side or the angle between the two given sides.

To solve for the angles $x$ and $y$, we would need one additional piece of information, such as the angle between the two sides, or the length of the third side. Without such data, we can't proceed with calculating the angles.

Could you provide any additional details, such as the missing angle or third side length, or should we assume this is an error in the setup of the problem? Let me know how you would like to proceed!