In the given figu

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°