Given the geometric configuration in the image and the relationship \( BAE + AED = CDE \), we need to find angle \( ABC \).

### Step 1: Understanding the Angles
1. **Labeling Angles**:
- Let \( \angle BAE = x \)
- Let \( \angle AED = y \)
- Then, based on the relationship \( x + y = \angle CDE \)

### Step 2: Finding Unknown Angles
2. **Analyzing Triangle BAE and AED**:
- The angles in triangle \( BAE \):
\[
\angle ABE + \angle BAE + \angle AEB = 180^\circ
\]
- The angles in triangle \( AED \):
\[
\angle AED + \angle EAD + \angle ACD = 180^\circ
\]
3. **Expressing Angles**:
- Since \( BAE + AED = CDE \), we can interpret this as:
\[
x + y = \angle CDE
\]

### Step 3: Solving for Angle \( ABC \)
4. **Using Properties of Angles**:
- If \( BAE + AED = CDE \), we can rewrite \( \angle ABC \):
\[
\angle ABC = 180^\circ - (x + y) = 180^\circ - \angle CDE
\]

### Conclusion:
The final expression for \( \angle ABC \) is determined by subtracting the sum \( x + y \) from \( 180^\circ \).

In summary, to find angle \( ABC \), you need to either calculate \( CDE \) directly or relate it to known angles in triangles \( BAE \) and \( AED \). If additional numerical values are provided for angles \( BAE \) and \( AED \), you can compute \( ABC \) more specifically.