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Question
In the following figure, if m(arc DXE) = 120° and m(arc AYC) = 60°. Find ∠DBE.
Solution
By inscribed angle theorem,
m∠AEB=(1/2) × m∠AYC=(1/2) × 60o = 30o ...(1)
m∠EAD=(1/2) × m∠DXE=(1/2) × 120o = 60o ...(2)
∠DBE + ∠AEB = ∠EAD ....(by Exterior Angle Theorem)
⇒ m∠DBE + 30o = 60o
⇒ m∠DBE = 60o - 30o = 30o
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