ABCD is a quadrilateral. CE and DE are the bisector of ∠C and ∠D respectively.
CE is the bisector of ∠C.
DE is the bisector of ∠D.
∠DCE + ∠CDE + ∠CED = 180° (Angle sum property)
In quadrilateral ABCD,
∠A + ∠B + ∠C + ∠D = 360° (Sum of angles of quadrilateral is 360°)
∴ ∠A + ∠B + 360° – 2∠CED = 360° [Using (3)]
⇒ ∠A + ∠B = 2 ∠CED