Question

The bisectors of angle B and angle C of an isosceles triangle ABC with AB=AC intersect each other at a point O. Show that the exterior angle adjacent to angle ABC =angle BOC.

Answer 1

Hello here is your answer by Sujeet yaduvanshi ☝☝☝☝☝☝



Solution:-ABD is the exterior angle adjacent to ∠ABC.

 

∠ABD + ∠ABC = 180°    (Linear pair)

 

⇒∠ABD = 180° – ∠ABC  … (1)

 

In ∆BOC,

∠OBC + ∠OCB + ∠BOC = 180°  (Angle sum property)



then,


1/2(∠ABC)+1/2(∠ACB)+∠BOC (2)


In ∆ABC

AB=AC(Given)

∠ACB=∠ABC. (3)
then,

From equation 1 and 2


1/2(∠ABC)+1/2(∠ACB)+∠BOC=180

so,

∠ABC+∠BOC=180

∠ABC=180-∠BOC. (4)


From equation 3 and 4


∠ABC=∠BOC



that's all

Answer 2

Here is hint for you

Angle boc=180-angle obc - angle ocb

=180 - 1/2 angle b- 1/2 angle c

=180-1/2 b- 1/2 b=180-b= angle and

Hope this will help you