O is the incentre of ABC and `angleA=30^(@)`. Accordingly what is `angleBOC`?

Options

A. `100^(@)`
B. `105^(@)`
C. `110^(@)`
D. `90^(@)`

Answer

To solve the problem of finding angle BOC when O is the incenter of triangle ABC and angle A is given as 30 degrees, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Incenter**: The incenter (O) of a triangle is the point where the angle bisectors of the triangle meet. It is also the center of the circle inscribed within the triangle.

2. **Identify the Angles**: We are given that angle A = 30 degrees. We need to find angle BOC.

3. **Use the Property of Angles**: The property of the angles related to the incenter states that:
\[ \angle BOC = 90^\circ + \frac{\angle A}{2} \]
This formula arises because the angles at the incenter are related to the angles of the triangle.

4. **Substitute the Given Angle**: Now, we can substitute the value of angle A into the formula:
\[ \angle BOC = 90^\circ + \frac{30^\circ}{2} \]

5. **Calculate the Value**:
\[ \angle BOC = 90^\circ + 15^\circ = 105^\circ \]

6. **Final Answer**: Therefore, the angle BOC is:
\[ \angle BOC = 105^\circ \]