Question

if one of the angles of a triangle is 130° then the angle between the bisector of the other two angles can be​

Answer 1

$\huge\tt{❥Answer♡}$

Consider a △ABC,such that ∠BAC=130° 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= 25

=> (∠ABC+∠ACB) = 25

=> ∠OBC+∠OCB = 25

━━━━━━━━━━━━━━━━━━━━━━━━━━━━

Now in OBC,

=> ∠OBC+∠OCB+∠BOC=180

=> 25+∠BOC=180

=> ∠BOC = 155°

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Answer 2

Answer:

Consider a △ABC,such that ∠BAC=130

∘

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

(∠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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