Question

One of the angles of a triangle is 68. The angle between the angle-bisectors of the other two angles is _____________

Answer 1

$\fcolorbox{aqua}{lime}{★Verified\: Answer}$

$\bold{Question}$

One of the angles of a triangle is 68. The angle between the angle-bisectors of the other two angles is _____________

$\bold{solution}$

Consider a △ABC,such that ∠BAC=68°

and bisectors of ∠B and ∠C meet at O.

To find: ∠BOC

Now, in △ABC,

∠BAC+∠ABC+∠ACB=180

68+∠ABC+∠ACB=180 (Angle sum property)

∠ABC+∠ACB=112

$\bold{\frac{1}{2}}$(∠ABC+∠ACB)=66

∠OBC+∠OCB=66 (OB and OC bisect ∠ABC and ∠ACB)

Now, in △OBC,

∠OBC+∠OCB+∠BOC=180

66+∠BOC=180

∠BOC=114°

${\tt{\pink{\underline{\underline{\huge{114°}}}}}}$

Answer 2

Answer:

Consider a △ABC,such that ∠BAC=68°

and bisectors of ∠B and ∠C meet at O.

To find: ∠BOC

Now, in △ABC,

∠BAC+∠ABC+∠ACB=180

68+∠ABC+∠ACB=180 (Angle sum property)

∠ABC+∠ACB=112

\bold{\frac{1}{2}}

2

1

(∠ABC+∠ACB)=66

∠OBC+∠OCB=66 (OB and OC bisect ∠ABC and ∠ACB)

Now, in △OBC,

∠OBC+∠OCB+∠BOC=180

66+∠BOC=180

∠BOC=114°

{\tt{\pink{\underline{\underline{\huge{114°}}}}}}

114°