Question

In the given figure:

(i) If ∠AOB = 45°, ∠BOC = 30° and ∠AOD= 110°; find : angles COD and BOD.
(ii) If ∠BOC = ∠DOC = 34° and ∠AOD = 120° ; find : angle AOB and angle AOC.
(iii) If ∠AOB = ∠BOC = ∠COD = 38° find : reflex angle AOC and reflex angle AOD.

Answer 1

(i) ∠COD = ∠AOD – ∠AOC

= ∠AOD – (∠AOB + ∠BOC)

= 110° - (45°+ 30°)

= 110°- 75°

= 35°

∠BOD = ∠AOD -∠AOB

= 110° - 45°

= 65°

(ii) ∠AOB = ∠AOD-∠BOD

= ∠AOD – (∠BOC + ∠COD)

= 120° – (34° + 34°)

= 120°-68°

= 52°

∠AOC = ∠AOB + ∠BOC

= 52° + 34°

= 86°

(iii) Reflex ∠AOC = 360°-∠AOC

= 360° – (∠AOB + ∠BOC)

= 360° – (38° + 38°)

= 360° – 76° = 284°

Reflex ∠AOD = 360° – ∠AOD

= 360° (∠AOB + ∠BOC + ∠COD)

= 360° – (38° + 38° + 38°)

= 360°- 114°

= 246°