Question

If one of the angles of a triangle is 150°, then find the angle between the bisectors of the other two angles.​

Answer 1

Answer:

Answer

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Correct option is

D

155o

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

21(∠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∘.

Answer 2

Answer:

155

o

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

∘

.

Step-by-step explanation:

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