Question

If one angle of a triangle is 130 then find the angle between the bisectors of the other two angles​

Answer 1

Let there be angles a ,b, c

a+b+c=180°

let a be 130

b+c=50°

ln the triangle formed by bisectors

1/2c+1/2b+d=180

since

b+c=50°

therefore

1/2c+1/2b=50/2°

1/2c+1/2b=25°

therefore

1/2c+1/2b+d=180

since

1/2c+1/2b=25°

therefore

d=155°

d is the angle between bisectors

Answer 2

Answer:

The angle between the bisectors of the other two angles is 155°

Step-by-step explanation:

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°

$\frac{1}{2}$ (∠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°

Hope this answer helps you out.