If I be the incentre of triangle ABC and `angleA=70^(@)` then find the value of `angleBIC`.

Answer

To find the value of angle \( BIC \) in triangle \( ABC \) where \( I \) is the incenter and \( \angle A = 70^\circ \), we can use the following steps:

### Step-by-Step Solution:

1. **Understand the Incenter**: The incenter \( I \) of triangle \( ABC \) is the point where the angle bisectors of the triangle intersect. It is equidistant from all sides of the triangle.

2. **Identify the Angles**: We know that \( \angle A = 70^\circ \). We need to find \( \angle BIC \).

3. **Use the Formula for Angle \( BIC \)**: The formula to find \( \angle BIC \) is:
\[ \angle BIC = 90^\circ + \frac{\angle A}{2} \]
This formula arises from the properties of the angles formed by the incenter and the vertices of the triangle.

4. **Substitute the Known Value**: Since \( \angle A = 70^\circ \):
\[ \angle BIC = 90^\circ + \frac{70^\circ}{2} \]

5. **Calculate \( \frac{70^\circ}{2} \)**:
\[ \frac{70^\circ}{2} = 35^\circ \]

6. **Add the Values**: Now, substitute back into the equation:
\[ \angle BIC = 90^\circ + 35^\circ = 125^\circ \]

### Final Answer:
\[ \angle BIC = 125^\circ \]

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