AB,CD and EF are three concurrent lines passung through the oint O such that OF bisects angleBOD . IF angleBOF = 35 degree ,find angleBOC and angleAOD

Answer :

Given , we have three concurrent lines AB , CD and EF , passing through point ' O ' And OF bisect $\angle$ BOD ,

$\angle$  BOF   =  35$°$ , So our figure is , As  :

And As given OF bisect ​$\angle$  BOD , so

$\angle$  BOF  =  ​$\angle$  FOD  =  $\frac{1}{2}$ ​$\angle$  BOD  =  35$°$                           ( As given $\angle$  BOF  = 35$°$ ) 

We know sum of all angles on a line is 180$°$ , So

$\angle$ BOF  +  $\angle$ FOD  + $\angle$ AOD  =  180$°$

35$°$  +  35$°$  +  $\angle$ AOD  =  180$°$

 $\angle$ AOD  =  110$°$                                                     ( Ans )

And 

 $\angle$  AOD and  $\angle$ BOC are opposite angles as formed by two line AB and CD  
And we know opposite angles are equal , So,

 $\angle$   AOD  =   $\angle$   BOC 
So,
 $\angle$   BOC  =  ​110$°$                                                      ( Ans )