Question

(b) In the given figure, AOB is the diameter, ACD and BED are straight lines. O is the centre of the
circle. <COE = 44 With reasons evaluate <CDE.

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Answer 1

∠CDE = 68°  In the given figure, AOB is the diameter, ACD and BED are straight lines. O is the centre of the circle. ∠COE = 44°

Step-by-step explanation:

in Δ OAC   & ΔOBE

OA = OC  ( Radius)    OB = OE  (Radius)

=> ∠OAC = ∠OCA    & ∠OBE = ∠OEB

∠OAC + ∠OCA + ∠AOC = 180°

=> 2∠OAC + ∠AOC = 180°

∠OBE + ∠OEB + ∠BOE = 180°

=> 2∠OBE + ∠BOE = 180°

adding both

=> 2∠OAC + ∠AOC  + 2∠OBE + ∠BOE = 180° + 180°

=> 2(∠OAC + ∠OBE) +  ∠AOC  + ∠BOE = 360°

∠AOC  + ∠BOE  + ∠COE = 180°  ( straight line)

=> ∠AOC  + ∠BOE + 44° = 180°

=> ∠AOC  + ∠BOE  = 136°

=> 2(∠OAC + ∠OBE) +  136° = 360°

=> ∠OAC + ∠OBE + 68° = 180°

∠BAD + ∠ABD + ∠ADB = 180°

=> ∠OAC + ∠OBE + ∠CDE = 180°

=> ∠CDE = 68°

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