In the given figure, ray OC is the bisector of `angleAOB` and OD is the ray opposite to OC. Show that `angleAOD=angleBOD`.

Explanation

Since OC is the bisector of `angleAOB`,
we have
`angleBOC=angleAOC`. ...(i)
Since ray OB stands on line DOC at a point O, we have
`angleBOC+angleBOD=180^(@)` ...(ii)
Again, ray OA stands on line DOC at a point O, so we have
`angleAOC+angleAOD=180^(@)` ...(iii)
From (ii) and (iii), we get
`angleAOC+angleAOD=angleBOC+angleBOD`
`implies angleAOD=angleBOD" "[ :' angleAOC=angleBOC" from (i)"]`.
Hence, `angleAOD=angleBOD`.