AB is a diameter of a circle with centre O. The tangent at a point C on the circle meets AB produced at Q. If ∠CAB = 42°, then what is the measure of ∠CBA ?

48°

OA and OC are radius of circle.

⇒ ∠QAC = ∠QCA = 42º

OC is radius of circle and form 90º angle at tangent QC.

∠QOC is exterior angle of triangle ACO .

So, ∠QOC = ∠QAC + ∠QCA 

= 42º + 42º

= 84º

In triangle CAQ,

∠CAQ + ∠CQA + ∠QCA = 180º

42º + 90º + ∠CQA  = 180º

∠CQA  = 48º