Given, ∠ACD and ∠BCD are linear pairs

CE and CF bisect ∠ACD and ∠BCD respectively

To prove:

∠ECF = 90°

⸫ ∠ACD + ∠BCD = 180° [Angle on a straight line]

⇒ ∠ACD/2 + ∠BCD/2 = 180°/2 = 90°

⇒ ∠ECD + ∠DCF = 90° [⸪ CE and CF bisect ∠ACD and ∠BCD respectively]

⸫ ∠ECD + ∠DCF = ∠ECF = 90°

Hence Proved.