The internal bisectors of `angleB and angleC` of `DeltaABC` meet at O. If `angleA=80^(@)` then `angleBOC` is :

Options

A. `50^(@)`
B. `160^(@)`
C. `100^(@)`
D. `130^(@)`

Answer

To find the measure of angle BOC in triangle ABC where the internal bisectors of angles B and C meet at point O and angle A is given as 80 degrees, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Triangle and Given Angles**:
We are given triangle ABC with angle A = 80 degrees. The internal bisectors of angles B and C meet at point O.

2. **Identify the Relationship Between Angles**:
The angle BOC is the angle formed at point O by the internal bisectors of angles B and C. We need to find the measure of angle BOC.

3. **Use the Property of Angles in a Triangle**:
The sum of the angles in a triangle is 180 degrees. Therefore, we can express angles B and C in terms of angle A:
\[ \angle B + \angle C = 180^\circ - \angle A = 180^\circ - 80^\circ = 100^\circ \]

4. **Let Angles B and C be Represented**:
Let angle B = x and angle C = y. From the previous step, we have:
\[ x + y = 100^\circ \]

5. **Find Angle BOC**:
The angle BOC can be expressed in terms of angles B and C using the formula:
\[ \angle BOC = 180^\circ - \frac{1}{2}(\angle A) \]
Substituting the value of angle A:
\[ \angle BOC = 180^\circ - \frac{1}{2}(80^\circ) = 180^\circ - 40^\circ = 140^\circ \]

6. **Final Calculation**:
Therefore, angle BOC is:
\[ \angle BOC = 140^\circ \]

### Conclusion:
The measure of angle BOC is 140 degrees.