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 step by step, we will find the angle between the 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:**
Let the angles of the triangle be \(A\), \(B\), and \(C\). Given that \(A = 130^\circ\), we need to find angles \(B\) and \(C\).

2. **Use the Angle Sum Property of a Triangle:**
The sum of the angles in a triangle is \(180^\circ\):
\[ A + B + C = 180^\circ \]
Substituting the value of \(A\):
\[ 130^\circ + B + C = 180^\circ \]
Simplifying this gives:
\[ B + C = 50^\circ \]

3. **Let \(B = x\) and \(C = y\):**
We can express \(B\) and \(C\) in terms of \(x\) and \(y\):
\[ x + y = 50^\circ \quad \text{(Equation 1)} \]

4. **Consider the Angles at the Bisectors:**
The angle between the bisectors of angles \(B\) and \(C\) can be represented as:
\[ \text{Angle between bisectors} = 180^\circ - \frac{1}{2}(B + C) \]
Substituting \(B + C\) from Equation 1:
\[ \text{Angle between bisectors} = 180^\circ - \frac{1}{2}(50^\circ) \]
Simplifying this gives:
\[ \text{Angle between bisectors} = 180^\circ - 25^\circ = 155^\circ \]

5. **Conclusion:**
The angle between the bisectors of the other two angles \(B\) and \(C\) is \(155^\circ\).

### Final Answer:
The angle between the bisectors of the other two angles can be \(155^\circ\).

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