Question

Ab cd ef are three concurrent lines passing through O such that OF bisects angle BOD. If angle BOF=35 degree find angle BOC and angle AOD

Answer 1

Given , we have three concurrent lines AB , CD and EF , passing through point ' O ' And OF bisect ∠ BOD ,  ∠  BOF   =  35° , So our figure is , As  :  And As given OF bisect ​∠  BOD , so  ∠  BOF  =  ​∠  FOD  =  12 ​∠  BOD  =  35°                           ( As given ∠  BOF  = 35° )   We know sum of all angles on a line is 180° , So  ∠ BOF  +  ∠ FOD  + ∠ AOD  =  180°  35°  +  35°  +  ∠ AOD  =  180°   ∠ AOD  =  110°                                                     ( Ans )  And    ∠  AOD and  ∠ BOC are opposite angles as formed by two line AB and CD   And we know opposite angles are equal , So,   ∠   AOD  =   ∠   BOC  So,  ∠   BOC  =  ​110°                                                      ( Ans )