Question
Two straight lines AB and CD intersect each other at a point O and angle AOC = 50° ; find:
(i) angle BOD
(ii) ∠AOD
(iii) ∠BOC
(i) angle BOD
(ii) ∠AOD
(iii) ∠BOC
✓
Answer
(i)∠BOD = ∠AOC
(Vertically opposite angles are equal)
∴ ∠BOD =50°
(ii) ∠AOD
∠AOD + ∠BOD = 180°
∠AOD + 50° = 180° [From (i)]
∠AOD = 180°-50°
∠AOD = 130°
(iii) ∠BOC = ∠AOD
(Vertically opposite angles are equal)
∴ ∠BOC =130°
(Vertically opposite angles are equal)
∴ ∠BOD =50°
(ii) ∠AOD
∠AOD + ∠BOD = 180°
∠AOD + 50° = 180° [From (i)]
∠AOD = 180°-50°
∠AOD = 130°
(iii) ∠BOC = ∠AOD
(Vertically opposite angles are equal)
∴ ∠BOC =130°
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