Circumcentre of ΔABC is O. If ∠BAC = 850, ∠BCA = 800, then ∠OAC is

In triangle ABC, the circumcenter O is equidistant from all vertices. By the central angle theorem, the angle subtended by an arc at the center is twice the angle at any point on the circumference. So angle BOC = 2 × angle BAC = 170°. Similarly, angle COA = 2 × angle CBA. First, angle ABC = 180° - 85° - 80° = 15°. Then angle COA = 2 × 15° = 30°. In triangle OAC, since OA = OC (radii), it is isosceles with angle OAC = angle OCA = (180° - 30°)/2 = 75°.