If one of the angles of a triangle is `130^(@)`, then the angle between the bisectors of the other two angles can be

Options

A. `50^(@)`
B. `65^(@)`
C. `145^(@)`
D. `155^(@)`

Explanation

To solve the problem, we need to find the angle between the angle bisectors of the other two angles in a triangle where one angle is given as \(130^\circ\).

### Step-by-Step Solution:

1. **Identify the Angles of the Triangle**:
We have a triangle \(ABC\) where \(\angle A = 130^\circ\). The other two angles are \(\angle B\) and \(\angle C\).

2. **Use the Triangle Angle Sum Property**:
The sum of the angles in a triangle is \(180^\circ\). Therefore, we can write:
\[ \angle A + \angle B + \angle C = 180^\circ \]
Substituting \(\angle A = 130^\circ\):
\[ 130^\circ + \angle B + \angle C = 180^\circ \]

3. **Solve for \(\angle B + \angle C\)**:
Rearranging the equation gives:
\[ \angle B + \angle C = 180^\circ - 130^\circ = 50^\circ \]

4. **Calculate Half of Angles B and C**:
Since we are interested in the angle between the bisectors of angles \(B\) and \(C\), we need to find \(\frac{1}{2} \angle B\) and \(\frac{1}{2} \angle C\). Let:
\[ \angle B = x \quad \text{and} \quad \angle C = 50^\circ - x \]
Therefore:
\[ \frac{1}{2} \angle B = \frac{x}{2} \quad \text{and} \quad \frac{1}{2} \angle C = \frac{50^\circ - x}{2} \]

5. **Find the Angle Between the Bisectors**:
The angle between the bisectors of angles \(B\) and \(C\) (denoted as \(\angle BOC\)) can be calculated using the formula:
\[ \angle BOC = 90^\circ + \frac{1}{2} \angle A \]
Substituting \(\angle A = 130^\circ\):
\[ \angle BOC = 90^\circ + \frac{130^\circ}{2} \]
\[ \angle BOC = 90^\circ + 65^\circ = 155^\circ \]

6. **Final Result**:
Therefore, the angle between the bisectors of angles \(B\) and \(C\) is:
\[ \angle BOC = 155^\circ \]

### Summary:
The angle between the bisectors of the other two angles in the triangle is \(155^\circ\).