Bisectors of the angles B and C of an isosceles `Delta ABC ` with AB=AC intersect each other at 0.Show that external angle adejcent to `angleABC "is equato" angleBOC.`

Explanation

Given `Delta ABC` is an isoseceles triangle in which AB=AC,BO and CO are the bisectors of `angleABC and angleACB ` respectively intersect at O.
To show `angleDBA=angleBOC `
Construction Line CB Produced to D

Proof in `Delta ABC " "AB=AC" "["given"]`
`angleACB=angleABC`
[angle opposite to equal sides are equal ]
`rArr " "(1)/(2)angleACB=(1)/(2)angleABC " "["on dividing both sides by 2"]`
`rArr " "angleOCB=angleOBC " "....(i)`
[`because `BO and CO are the bisectors of `angleABC and angleACB`]
In `DeltaBOC,angleOBC+angleOCB+angleBOC=180^(@) " "["by angle sum propert of a triangle"]`
`rArr " " angleOBC+angleOBC+angleBOC=180^(@) " "["from Eq.(i)"]`
`rArr " "2angleOBC+angleBOC=180^(@)`
`rArr " " angleABC+angleBOC=180^(@)" "[because "BO is the bisector of " angleABC ]`
`rArr " "180^(@)-angleDBA+angleBOC=0`
`rArr " " angleDBA=angleBOC`