Question

Prove that the bisectors of the angle of a linear pair are at right angles

Answer 1

Angles ACD and DCB are a linear pair. Sum of these angles = 180 deg

ACD + DCB = 180 deg

CE is bisector of angle ACD.

CF is bisector of angle DCB.

To prove that angle ECF = 90 deg.

ECF = ECD + DCF = 1/2 ACD + 1/2 DCB

         = 1/2 { angle ACD + angle DCB ] = 1/2 180 deg = 90 deg