Answered

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

Sagot :

Given data:

The given figure of the circle.

The angle DCA is,

[tex]\begin{gathered} \angle DCA=\frac{1}{2}\angle AOD \\ =\frac{1}{2}(114^{\circ}) \\ =57^{\circ} \end{gathered}[/tex]

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

[tex]\begin{gathered} \angle DBC=90^{\circ}-40^{\circ} \\ =50^{\circ} \end{gathered}[/tex]

The angle BOC is,

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

Thus, the third option is correct.

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