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In DeltaABC, bisectors of angleB and ang...

In `DeltaABC`, bisectors of `angleB and angleC` interesct each other at point O. Prove that `angleBOC=90^(@)+(1)/(2)angleA i.e., angle1 =90^(@)+(1)/(2)`

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In `DeltaOBC`,
`angle1+angle3+angle4=180^(@)` (angle sum property )....(1)
In `DeltaABC`,
`angleA+angleBangleC=180^(@)" "` (angle sum property)

`rArr (1)/(2)angleA +(1)/(2)angleB+(1)/(2)angleC=90^(@)`
`rArr (1)/(2)angleA+angle4=90^(@)" "` ( `:. Bo and CO` are bisectores of `angleB and angleC`)
`rArr(1)/(2)angle+180^(@)-angle1=90^(@)" "` [from (1)]
`rArr angle1=180^(@)-90^(@)+(1)/(2)angleA`
`rArr angle1 =90^(@)+(1)/(2)`
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