Question

If one angle of triangles is 130°, find the angle between the bisectors of the other two angles

Answer 1

Let the x and y be the bisected angles
so in the original triangle sum of angles is
130 + 2x + 2y = 180
=> 2(x+y) = 50
=> x + y = 25

Answer 2

Answer:

Step-by-step explanation:

Consider a △ABC,such that ∠BAC=130  

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 and bisectors of ∠B and ∠C meet at O.

To find: ∠BOC

Now, in △ABC,

∠BAC+∠ABC+∠ACB=180

130+∠ABC+∠ACB=180 (Angle sum property)

∠ABC+∠ACB=50

2

1

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(∠ABC+∠ACB)=25

∠OBC+∠OCB=25 (OB and OC bisect ∠ABC and ∠ACB)

Now, in △OBC,

∠OBC+∠OCB+∠BOC=180

25+∠BOC=180

∠BOC=155  

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