Question
Use the adjoining figure to find: (i) ∠BOD (ii) ∠AOC
✓
Answer
∠AOD = 72°
∠BOC = 64°
But sum of angles on the same side of a line = 180°
∴ ∠AOD + ∠COD + ∠BOC = 180°
72° + ∠COD + 64° = 180°
∠COD = 180° - (72° + 64°)
= 180° - 136° = 44°
(i) Now ∠BOD = ∠BOC + ∠COD
= 64° + 44° = 108°
(ii) ∠AOC = ∠AOD + ∠COD
= 72° + 44° = 116°
∠BOC = 64°
But sum of angles on the same side of a line = 180°
∴ ∠AOD + ∠COD + ∠BOC = 180°
72° + ∠COD + 64° = 180°
∠COD = 180° - (72° + 64°)
= 180° - 136° = 44°
(i) Now ∠BOD = ∠BOC + ∠COD
= 64° + 44° = 108°
(ii) ∠AOC = ∠AOD + ∠COD
= 72° + 44° = 116°
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