PAQ is a tangent to a circle with center O, at a point A unit. AB is a chord such that ∠BAP = x° (x < 90°). C is a point on the major arc AB such that ∠ACB = y°. If ∠ABO = 35°, then the value of x + y is :

110°

AO = BO

⇒ ABO = ∠BAO = 35°

and ∠OAQ = 90° (angle by radius on tangent)

⇒ x° + 35° = 90°

x° = 55°

and we know, x° = y°

⇒ x + y = 55 + 55 = 110°