Question

In the given figure, o is the centre

Answer 1

angle BCE = angle BAD = 85......exterior angle of a cyclic quadrilateral is always equal to the opposite interior angle
angle BOD = 2 angle BAD.....inscribed angle theorem.
therefore angle BOD = 2* 85' = 170'

Answer 2

1)ABCD is a cyclic quadrilateral.

/_BAD = /_BCE
(angle opp to ext. /_is equal)
/_BAD = 85°
===============================
now
2)
/_BCE + /_BCD = 180°
[linear pair]
/_BCD = 180°-/_BCE
=180°-85
=95°

now

reflex BOD = 2(BCD)
[/_at center = 2(/_at circumference)
=2(95°)
=190°

now
/_BOD = 360°-190° = 170°