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If one of the angles of a triangle is $130^{0}$ , then the angle between the bisectors of the other two angles can be

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50^{0}

65^{0}

145^{0}

155^{0}

answer is D.

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Detailed Solution

Given, one of the angles of a triangle is

130^{0}

.
Let

x

and

y

be the bisected angles as in the following figure.
Question Image

So, in the original triangle, sum of angles

= 180^{o}

.
Therefore,

2 x + 2 y + 130 = 180

\Rightarrow 2 (x + y) = 50

\Rightarrow x + y = 25

°
In the smallest triangle, consisting of original side opposite

130^{o}

.
Therefore,

25^{o} +

angle between bisectors

= 180^{o}

.
Angle between bisectors of other two angles

= 155^{o}

.
Hence, the correct option is 4.

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