In `/_\\` ABC, side BC has been produced to D such that `/_ACD = 125^circ and angleBAC = 60^circ. Then, /_`ABC =?

Options

A. `55^(@)`
B. `60^(@)`
C. `65^(@)`
D. `70^(@)`

Answer

To solve the problem, we need to find the measure of angle ABC in triangle ABC, given that angle ACD is 125° and angle BAC is 60°.

### Step-by-Step Solution:

1. **Identify the Angles**:
- We are given:
- Angle ACD = 125°
- Angle BAC = 60°

2. **Understand the Exterior Angle Theorem**:
- The Exterior Angle Theorem states that the measure of an exterior angle (in this case, angle ACD) is equal to the sum of the measures of the two opposite interior angles (angles ABC and BAC).
- Mathematically, this can be expressed as:
\[ \text{Angle ACD} = \text{Angle ABC} + \text{Angle BAC} \]

3. **Set Up the Equation**:
- Substitute the known values into the equation:
\[ 125° = \text{Angle ABC} + 60° \]

4. **Solve for Angle ABC**:
- Rearranging the equation gives us:
\[ \text{Angle ABC} = 125° - 60° \]
- Calculate the right side:
\[ \text{Angle ABC} = 65° \]

5. **Conclusion**:
- Therefore, the measure of angle ABC is 65°.

### Final Answer:
\[ \text{Angle ABC} = 65° \]