PAQ is a tangent to circle with centre O, at a point A on it. AB is a chord such that $\angle B A Q=x^{\circ}(x<90)$. C is a point on the major arc AB such that $\angle A C B=y^{\circ}$. If $\angle A B O=32^{\circ}$, then the value of x + y is:

116

OA is radius of circle and makes 90º with tangent.

∠OAQ = 90º

∠OAQ = ∠OAB + ∠BAQ

90º = 32º + ∠BAQ

{ OA = OB ⇒ ∠OAB = ∠ABO }

∠BAQ = 58º 

By using alternate segment theorem ,

∠BAQ = ∠ACB 

Hence , ∠ACB = 58º 

Now, x + y = 58º + 58º  = 116º