Question

If one of the angle of a triangle is 120degree , then the angle between the bisectors of the other two angles can be

Answer 1

maybe.. two angle can be 60 degree..

Answer 2

Given info : one of the angle of a triangle is 120°.

To find : the angle between the bisectors of the other two angles can be ..

solution : see diagram, let ABC is a triangle where ∠A = 120° , line BP and line CP are bisectors of angle ∠B and ∠C respectively join at point P.

now we have to find the angle ∠BPC = ?

we know, sum of all angles of a triangle is 180°

∴ ∠A + ∠B + ∠C = 180°

⇒ 120° + ∠B + ∠C = 180°

⇒ ∠B + ∠C = 60° ...(1)

as BP and CP are angle bisectors of ∠B and ∠C respectively.

so, ∠PBC = 2∠B and ∠PCB = ∠C

now from ΔPBC,

⇒ ∠BPC + ∠PBC + ∠PCB = 180°

⇒ ∠BPC + 2∠B + 2∠C = 180°

⇒ ∠BPC + 2(∠B + ∠C) = 180°

⇒ ∠BPC = 180° - 2(60°) = 60° [ from eq (1) ]

therefore the angle between the bisectors of the other two angles is 60°