In the following figure, if m(are DXE) = 90° and m(are AYC) = 30°. Find ∠DBE.

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#### Solution

By inscribed angle theorem,

m∠AEB=(1/2) × m∠AYC=(1/2) × 30^{o} = 15^{o }...(1)

m∠EAD=(1/2) × m∠DXE=(1/2) × 90^{o} = 45^{o} ...(2)

∠DBE + ∠AEB = ∠EAD

⇒ m∠DBE + 15^{o} = 45^{o}

⇒ m∠DBE = 45^{o} - 15^{o} = 30^{o}

Concept: Areas of Sector and Segment of a Circle

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