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