In the given figure, O is the centre of a circle and ∠ = 50°. Then, ∠BOD = ?
Given: ∠OAB = 50°
Consider ΔAOB
Here,
OA = OB (radius)
∠OAB = ∠OBA = 50° (In a triangle, angles opposite to equal sides are equal)
By angle sum property
∠AOB + ∠OAB + ∠OBA = 180°
∠AOB + 50° + 50° = 180°
∠AOB = 180° – 50° – 50°
∠AOB = 80°
Here,
∠AOD = ∠AOB + ∠BOD
180° = 80° + ∠BOD
∠BOD = 180° – 80° = 100°
∴ ∠BOD = 100°