If one of the angles of a triangle is 130o, then the angle between the bisectors of the other two angles can be,

It is given that one of the angles of a triangle is

130^{o} .

We know that the angle sum property of a triangle states that the sum of interior angles of a triangle is 180°.

Let’s consider a triangle ABC. Then we have,

∠ A + ∠ B + ∠ C = 180^{\circ} (1)

Given that,

∠ A = 130^{\circ}

Therefore, from equation (1), we have,

130^{\circ} + ∠ B + ∠ C = 180^{\circ}

\Rightarrow ∠ B + ∠ C = 50^{\circ}

\Rightarrow \frac{∠ B}{2} + \frac{∠ C}{2} = 25^{\circ} (2)

Let OB and OC are the angle bisector of

∠ B

and

∠ C

respectively.
In triangle OBC, we have,

∠ OBC + ∠ OCB + ∠ BOC = 180^{\circ}

\Rightarrow \frac{∠ B}{2} + \frac{∠ C}{2} + ∠ BOC = 180^{\circ}

\Rightarrow 25^{\circ} + ∠ BOC = 180^{\circ}

\Rightarrow ∠ BOC = 155^{\circ}

Thus, the angle between bisectors of other two angles can be

155^{o}

.
Hence, option (4) is correct.

If one of the angles of a triangle is $130^{o}$ , then the angle between the bisectors of the other two angles can be,