Question

In the given figure, XAY is a tangent to the circle centered at O. If ∠ABO = 40°, then find ∠BAY and ∠AOB.

Answer 1

Given, ∠ABO = 40°

∠XAO = 90°  ...(Angle between radius and tangent)

OA = OB  ...(Radii of same circle)

⇒ ∠OAB = ∠OBA

∴  ∠OAB = 40°

Now, applying the linear pair of angles property,

we get

∠BAY + ∠OAB + ∠XAO = 180°

⇒ ∠BAY + 40° + 90° = 180°

⇒ ∠BAY + 130° = 180°

⇒ ∠BAY = 180° – 130°

⇒ ∠BAY = 50°

Now, In ΔAOB,

∠AOB + ∠OAB + ∠OBA = 180°

or, ∠AOB + 40° + 40° = 180°

or, ∠AOB = 180° – 80° = 100°