Question

O is a point inside a triangle ABC.prove that angle BOC= angle BAC+angleABO+angleACO

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]