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Bisectors of the angles B and C of an is...

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

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In `DeltaABC`, we have `AB=AC`
`:. angleB=angleC` (`:'` angles opposite to equal sides of a triangle are equal)
`:. 1/2 angleB=1/2 angleC` ...(1)
In `DeltaOBC`, we have
`angle1=1/2angleB` and `angle2=1/2 angleC`
`:. angle1=angle2` [from (1)]
`angleDBC+angle1+angleOBA=180^(@)" "[ :' ABD" is a straight line"]`
`implies" "angleDBC+2angle1=180^(@)" "[ :' angle1=angleOBA]` ...(2)
In `DeltaOBC`,
`angle1+angle2+angeBOC=180^(@)" "[ :. angle1=angle2]` ...(3)
From (2) and (3), we get
`angleDBC+2angle1+angleBOC`
`implies" "angleDBC=angleBOC`
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