Question

In the following figure, if m(arc DXE) = 120° and m(arc AYC) = 60°. Find ∠DBE.

Answer 1

By inscribed angle theorem,

m∠AEB=(1/2) × m∠AYC=(1/2) × 60^o = 30^o ...(1)

m∠EAD=(1/2) × m∠DXE=(1/2) × 120^o = 60^o ...(2)

∠DBE + ∠AEB = ∠EAD   ....(by Exterior Angle Theorem)

⇒ m∠DBE + 30^o = 60^o

⇒ m∠DBE = 60^o - 30^o = 30^o