Given AB is a circle and BT is a tangent, ∠BAO=32° Here, ∠OBT=90° [∵ Tangent is ⊥ to the radius at the point of contact] OA=OB [ Radii of the same circle] ∴ ∠OBA=∠OAB=32° [ Angles opposite to equal side are equal] ∴ ∠OBT=∠OBA+∠ABT=90° or 32°+x=90° ∠x=90°−32°=58° Also, ∠AOB=180°−∠OAB−∠OBA =180°−32°−32°=116° Now Y=
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AOB [ Angle formed at the center of a circle is double the angle formed in the remaining part of the circle] =