Question

If O is a point inside a ∆ABC prove that angle BOC=angle BAC + angle ABO + angle ACO​

Answer 1

In triangle ABC,

<BAC + <ABC + < ACB = 180

or <BAC + (<ABO + <OBC) + (<ACO + <OCB) = 180

or <OBC + <OCB = 180 - (<BAC + <ABO + <ACO) ----(1)

In triangle BOC,

<OBC + <OCB + <BOC = 180

or 180 - (<BAC + <ABO + <ACO) + <BOC = 180   (from (1))

or - <BAC - <ABO - <ACO + <BOC = 0

or <BOC = <BAC + <ABO + <ACO [proved]