In the given figure, CE||BA. If `/_BAC = 70^(@)` and `/_ECD = 50^(@)`,find `/_`ACB.

Answer

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

### Step-by-Step Solution:

1. **Identify Given Information:**
- CE is parallel to BA (CE || BA).
- Angle BAC = 70°.
- Angle ECD = 50°.

2. **Use Alternate Angles Property:**
- Since CE is parallel to BA, the angles BAC and ACE are alternate interior angles.
- Therefore, angle ACE = angle BAC = 70°.

3. **Set Up the Equation for Angles on a Straight Line:**
- On the straight line CE, the sum of angles ACE, ACB, and ECD must equal 180°.
- This can be expressed as:
\[ \text{Angle ACE} + \text{Angle ACB} + \text{Angle ECD} = 180° \]

4. **Substitute Known Values:**
- Substitute the known values into the equation:
\[ 70° + \text{Angle ACB} + 50° = 180° \]

5. **Combine Like Terms:**
- Combine the angles on the left side:
\[ 120° + \text{Angle ACB} = 180° \]

6. **Solve for Angle ACB:**
- Isolate angle ACB:
\[ \text{Angle ACB} = 180° - 120° = 60° \]

### Final Answer:
- Angle ACB = 60°.

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