O is centre of the cricle. If `angle AOD= 40^(@) and angle ACB=35^(@)`, then the find the value of `angle BCO and angleBOD`.

Explanation

The central angle produced by the are `overset(frown)(AB)= angleAOB and` the angle in circle `=angleACB= 35^(@)` (Given)
`:.` by theroem -34 `angleAOB=2 angle ACB= 2xx 35^(@)=70^(@)`
Again, the central angle produced by `overset( frown)(AD)= angleAOD` and angle in cricle = `angleACD or angle ACO`.

`:.` by theorem-34 ` angle =2 angle ACO`
or, `40^(@)=2 angle ACO [ :. angle AOD=40^(@)` ( Given)]
or, `angle ACO=(40^(@))/(2)=20^(@),`
Now, `angle BCO= angle ACB+ angle ACO=35^(@)+20^(@)=55^(@)[ :. angle ACB=35^(@) ("Given") and angle ACO=20^(@)]`
and `angle BOC= angle AOB+ angle AOB=40^(@)+70^(@)=110^(@)[ :. angle AOB=40^(@) ("Given") and angle AOB=70^(@)]`
`:. angle BCO= 55^(@) and angle BOD= 110^(@)`