In a `Delta ABC`, I is incenter, `angle BIC=116^(@)` find `angle A`.

Answer

To find angle A in triangle ABC where I is the incenter and angle BIC is given as 116°, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Relationship**: In a triangle, the angle formed at the incenter (angle BIC) can be expressed in terms of the angles of the triangle. The relationship is given by the formula:
\[ \angle BIC = 90^\circ + \frac{\angle A}{2} \]

2. **Substitute the Known Value**: We know that angle BIC is 116°. Substitute this value into the formula:
\[ 116^\circ = 90^\circ + \frac{\angle A}{2} \]

3. **Isolate the Angle A Term**: To isolate \(\frac{\angle A}{2}\), subtract 90° from both sides:
\[ 116^\circ - 90^\circ = \frac{\angle A}{2} \]
\[ 26^\circ = \frac{\angle A}{2} \]

4. **Solve for Angle A**: Multiply both sides by 2 to find angle A:
\[ \angle A = 26^\circ \times 2 = 52^\circ \]

5. **Final Answer**: Therefore, the measure of angle A is:
\[ \angle A = 52^\circ \]