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:
Answer & explanation
Correct answer: option 4
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