Ques.No.1
In DeltasABO and COD
/_AOB=/_COD - vertically opposite angles
/_ABO=/_DCO - alternate opposite angles as AB||CD
/_BAO=/_ODC - alternate opposite angles as AB||CD
As such DeltasABO and COD are similar and hence
(CO)/(OB)=(CD)/(AB) i.e. x/2=12/4
and x=12/4xx2=6 cm.
Ques.No.2
As AB||CE and AC is transverse /_a=70^@ as they are alternate interior angles.
Further as AB||CE and BC is transverse /_b=/_c as they are corresponding angles.
Now in DeltaABC, we have AB=AC, hence /_ACB=/_ABC=b^@
Hence 2b^@+a^@=2b^@+70^@=180^@
or 2b^@=180^@-70^@=110^@ i.e. b=55
and as /_c=/_b=55^@, c=55