Question

Points A, B, C, and D are on circle O, as shown.

Answer 1

Given data:

The given figure of the circle.

The angle DCA is,

`\begin{gathered} \angle DCA=(1)/(2)\angle AOD \\ =(1)/(2)(114^(\circ)) \\ =57^(\circ) \end{gathered}`

BD is diameter , it means the angle BCD is 90 degrees, the angle DBC is,

`\begin{gathered} \angle DBC=90^(\circ)-40^(\circ) \\ =50^(\circ) \end{gathered}`

The angle BOC is,

`\begin{gathered} \angle BOC=180^(\circ)-2\angle\text{OBC} \\ =180^(\circ)-2\angle DBC \\ =180^(\circ)-2(50^(\circ)) \\ =80^(\circ) \end{gathered}`

Thus, the third option is correct.