Question

The bisectors of ZB and ZC of an isosceles AABC with AB = AC intersect each other at a point O. Show that the exterior angle adjacent to ZABC
is equal to ZBOC.

Figure is not given in book..​

Answer 1

Step-by-step explanation:

Given BD is Bisector of ∠ABC and CO is Bisector of ∠ACB produce CB to D

In ΔABC

AB=AC

∠ACB=∠ABC

2

1

∠ACB=

2

1

∠ABC

∠OCB=∠OBC

in ΔBOC

∠OBC+∠OCB+∠BDC=180

∘

2∠OBC+∠BOC=180

∘

∠ABC+∠BOC=180

∘

∠ABC+∠OBA=180

∘

∠DBA=∠BOC