AB is a chord to a circle and PAT is the tangent to the circle at A. If ?BAT = 750 and ?BAC= 450 ,C being a point on the circle then, ?ABC is equal to-

Given: AB is a chord, PAT is tangent at A, angle BAT = 75°, and angle BAC = 45°. By the alternate segment theorem, angle between tangent and chord equals angle in the alternate segment. Therefore angle BAT = angle ACB = 75°. In triangle ABC, angle BAC = 45° (given) and angle ACB = 75° (from tangent-chord theorem). The sum of angles in a triangle is 180°, so angle ABC = 180° - (45° + 75°) = 180° - 120° = 60°. Option A (75°) is angle BAT, not angle ABC. Option B (45°) is angle BAC.