Answer: The answer is (C) 47.5.
Step-by-step explanation: In the given figure, O is the centre of a circle, where AC is the diameter and OB is the radius. We are to find the measure of ∠BAC.
We have
[tex]m\angle AOB+m\angle BOC=180^\circ\\\\\Rightarrow m\angle BOC=180^\circ-85^\circ\\\\\Rightarrow m\angle BOC =95^\circ.[/tex]
∠BOC and ∠BAC are angles at the centre and at the circumference subtended by the arc BC, so
[tex]m\angle BAC=\dfrac{1}{2}\times m\angle BOC=\dfrac{1}{2}\times 95^\circ=47.5^\circ.[/tex]
Thus, (C) is the correct option.
