In `Delta ABC, angle A = 58^(@)`. If I is the incentre of the triangle, then the measure `angle BIC` is :

Options

A. `119^(@)`
B. `112^(@)`
C. `109^(@)`
D. `123^(@)`

Answer

To find the measure of angle \( BIC \) in triangle \( ABC \) where \( \angle A = 58^\circ \) and \( I \) is the incenter, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Properties of the Incenter**:
The incenter \( I \) of a triangle is the point where the angle bisectors of the triangle meet. The angle \( BIC \) can be calculated using the formula:
\[ \angle BIC = 90^\circ + \frac{\angle A}{2} \]

2. **Substitute the Value of Angle A**:
Given that \( \angle A = 58^\circ \), we can substitute this value into the formula:
\[ \angle BIC = 90^\circ + \frac{58^\circ}{2} \]

3. **Calculate Half of Angle A**:
Calculate \( \frac{58^\circ}{2} \):
\[ \frac{58^\circ}{2} = 29^\circ \]

4. **Add to 90 Degrees**:
Now, add \( 90^\circ \) to \( 29^\circ \):
\[ \angle BIC = 90^\circ + 29^\circ = 119^\circ \]

5. **Final Answer**:
Therefore, the measure of angle \( BIC \) is:
\[ \angle BIC = 119^\circ \]