Question

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

Answer 1

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