In a `DeltaABC`, the bisectors of `angleB and angleC` meet at point O within the triangle. If `angleA = 132^(@)` then the measure of `angleBOC` is(in degrees) :

Options

A. `166^(@)`
B. `84^(@)`
C. `156^(@)`
D. `120^(@)`

Answer

To solve the problem, we need to find the measure of angle BOC in triangle ABC, given that angle A = 132 degrees. We will use the property of the incenter of a triangle, which is where the angle bisectors of the triangle meet.

### Step-by-Step Solution:

1. **Identify the Given Information**:
- We have triangle ABC.
- Angle A = 132 degrees.
- O is the point where the angle bisectors of angles B and C meet.

2. **Understand the Incenter Property**:
- The point O is the incenter of triangle ABC.
- The angle BOC can be calculated using the formula:
\[ \text{Angle BOC} = 90^\circ + \frac{\text{Angle A}}{2} \]

3. **Substitute the Value of Angle A**:
- We know angle A = 132 degrees.
- Substitute this value into the formula:
\[ \text{Angle BOC} = 90^\circ + \frac{132^\circ}{2} \]

4. **Calculate the Half of Angle A**:
- Calculate \(\frac{132^\circ}{2}\):
\[ \frac{132^\circ}{2} = 66^\circ \]

5. **Add 90 degrees to Half of Angle A**:
- Now, add 90 degrees to 66 degrees:
\[ \text{Angle BOC} = 90^\circ + 66^\circ = 156^\circ \]

6. **Final Answer**:
- Therefore, the measure of angle BOC is:
\[ \text{Angle BOC} = 156^\circ \]

### Conclusion:
The measure of angle BOC is 156 degrees.