The image you've provided includes a geometric figure—a triangle—and asks to find the values of $x$ and $y$. It also gives some information:

• The angle at point $A$ is $49^\circ$.
• $AB$ and $BC$ have equal lengths, as indicated by the tick marks.
• The side $AD = 6$.
• The sides opposite $x$ and $y$ are labeled, and the triangles involved seem to suggest use of trigonometry or properties of isosceles triangles.

Here’s how we approach this:

1. Recognize the Triangle Properties:

   • The triangle $ABC$ looks like an isosceles triangle because the sides $AB = BC$ are equal.
   • The sum of angles in any triangle must be $180^\circ$.
   • We are given angle $A = 49^\circ$, so the other two angles at $B$ and $C$ should add up to $131^\circ$, and since triangle $ABC$ is isosceles, each of these angles should be equal.
   • So, the angle at $B$ and $C$ will be $\frac{131^\circ}{2} = 65.5^\circ$.

2. Relation of Sides Using Trigonometry: If we have enough information, we could use the law of sines or cosines to find the unknowns $x$ and $y$, but the exact approach will depend on the triangle configuration.

Would you like further steps to apply a specific method, or is there more information available in the problem?

Expanding on the situation:

1. What are the full angle measures in triangle $ABC$?
2. Are there any additional angle or side measures not visible in the image?
3. What trigonometric relationships can we use to solve for $x$ and $y$?
4. How do we use the isosceles triangle property to solve this?
5. What laws of sines or cosines can be useful here?

Tip: Always check for symmetry in triangles and apply properties like equal angles or sides when possible!