In `DeltaABC,angleA=68^(@)` .If I is the incentre of the triangle ,then the measure of `angle` BIC is :

Options

A. `124^(@)`
B. `68^(@)`
C. `54^(@)`
D. `148^(@)`

Answer

To find the measure of angle BIC in triangle ABC where angle A is given as 68 degrees, we can use the formula related to the incenter of the triangle.

### Step-by-Step Solution:

1. **Identify the Given Information**:
- We have triangle ABC with angle A = 68 degrees.
- I is the incenter of triangle ABC.

2. **Recall the Formula**:
- The formula for the angle BIC is given by:
\[ \angle BIC = 90^\circ + \frac{1}{2} \angle A \]

3. **Substitute the Value of Angle A**:
- Substitute angle A = 68 degrees into the formula:
\[ \angle BIC = 90^\circ + \frac{1}{2} \times 68^\circ \]

4. **Calculate Half of Angle A**:
- Calculate \(\frac{1}{2} \times 68^\circ\):
\[ \frac{1}{2} \times 68^\circ = 34^\circ \]

5. **Add to 90 Degrees**:
- Now, add 90 degrees to 34 degrees:
\[ \angle BIC = 90^\circ + 34^\circ = 124^\circ \]

6. **Conclusion**:
- Therefore, the measure of angle BIC is \(124^\circ\).

### Final Answer:
\[ \angle BIC = 124^\circ \]