$$\eqalign{
& a)\,\,Goi\,\,OC\,\,la\,\,tia\,\,phan\,\,giac\,\,cua\,\,\widehat {AOB} \cr
& \Rightarrow \widehat {AOC} = \widehat {BOC} \cr
& Ta\,\,co:\,\,\,\widehat {B'OC} = \widehat {B'OB} - \widehat {BOC} = {90^0} - \widehat {BOC} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\widehat {A'OC} = \widehat {A'OA} - \widehat {AOC} = {90^0} - \widehat {AOC} \cr
& Ma\,\,\widehat {AOC} = \widehat {BOC} \Rightarrow {90^0} - \widehat {AOC} = {90^0} - \widehat {BOC} \cr
& \Rightarrow \widehat {B'OC} = \widehat {A'OC} \Rightarrow \,OC\,\,la\,\,tia\,\,phan\,\,giac\,\,cua\,\,\widehat {A'OB'} \cr
& b)\,\,\widehat {AOB} + \widehat {A'OB'} \cr
& = 2\widehat {BOC} + 2\widehat {B'OC} \cr
& = 2\left( {\widehat {BOC} + \widehat {B'OC}} \right) \cr
& = 2\widehat {B'OB} = {2.90^0} = {180^0} \cr} $$
