The image contains a geometric diagram with points labeled $A$, $B$, $C$, $D$, and $E$, forming what appears to be two intersecting triangles. The task is to find $\angle DCE$.

From the diagram:

• $A$, $B$, and $C$ appear to be part of a smaller triangle with $B$ at the intersection of the lines.
• $C$ seems to be an interior angle of triangle $DCE$, with $\angle DCE$ being requested.
• There seems to be an angle $\angle ABC$ marked as $60^\circ$, and $\angle BCA$ is marked $90^\circ$, which might help in determining the relationship between the angles.

Given the right angle at $C$ in triangle $ABC$, we can deduce angle properties from there, but I need more context or any missing measurements to compute $\angle DCE$.

Could you confirm or provide more details about the problem setup? For example, do we have specific angle values for the remaining parts of the diagram?

Would you like a detailed solution based on these observations or further clarifications?

Here are some related questions for further exploration:

1. What other angles are provided in the problem (e.g., angles $\angle DCE$ or $\angle ABC$)?
2. Is $\triangle ABC$ similar to $\triangle DCE$, or are they part of the same geometric structure?
3. Could additional properties such as parallel lines or angle bisectors be involved?
4. How does the marked $60^\circ$ angle relate to the rest of the figure?
5. Are any side lengths or proportional relationships between sides given?

Tip: In many geometry problems, using properties like angle sum in triangles or transversals with parallel lines can simplify finding unknown angles.