Question

Help. Find mBAC in circle O. (The figure is not drawn to scale.)

Answer 1

C: 47.5 is the answer 

Answer 2

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

$m\angle AOB+m\angle BOC=180^\circ\\\\\Rightarrow m\angle BOC=180^\circ-85^\circ\\\\\Rightarrow m\angle BOC =95^\circ.$

∠BOC and ∠BAC are angles at the centre and at the circumference subtended by the arc BC, so

$m\angle BAC=\dfrac{1}{2}\times m\angle BOC=\dfrac{1}{2}\times 95^\circ=47.5^\circ.$

Thus, (C) is the correct option.