15. ∠BOD = 80°, ∠AOB = 3 ∠AOD, OC — биссектриса ∠AOB, ∠COD - ?

∠AOB = 3 ∠AOD, ∠AOD + ∠BOD = ∠AOB = 3 ∠AOD

∠BOD = 3 ∠AOD - ∠AOD = 2 ∠AOD

∠AOD = ∠BOD/2 = 80°/2 = 40°

∠AOB = 3 ∠AOD = 3 × 40° = 120°

∠AOC = ∠BOC = ∠AOB/2 = 120°/2 = 60°

∠COD = ∠BOD - ∠BOC = 80° - 60° = 20°

Ответ: ∠COD = 20°