In the given figure, side BC of `/_\ ABC` is produced to D and CE||BA. If `/_BAC = 50^(@)`,then `/_ACE` = ……

Answer

To solve the problem step by step, we will use the properties of parallel lines and angles.

### Step-by-Step Solution:

1. **Identify the Given Information:**
- We are given that angle \( \angle BAC = 50^\circ \).
- Line segment \( CE \) is parallel to line segment \( AB \).
- Line segment \( BC \) is extended to point \( D \).

2. **Understand the Relationship Between Angles:**
- Since \( CE \) is parallel to \( AB \) and \( AC \) acts as a transversal line, we can apply the properties of alternate interior angles.

3. **Apply the Alternate Interior Angles Theorem:**
- According to the Alternate Interior Angles Theorem, if two parallel lines are cut by a transversal, then the alternate interior angles are equal.
- Therefore, \( \angle BAC \) (which is \( 50^\circ \)) is equal to \( \angle ACE \).

4. **Conclude the Value of Angle \( ACE \):**
- Since \( \angle BAC = 50^\circ \), we can conclude that:
\[ \angle ACE = \angle BAC = 50^\circ \]

### Final Answer:
\[ \angle ACE = 50^\circ \]