Question

Prove that the bisectors of the angles of a linear pair are at right angles...
Please answer fast, it's urgent...

Answer 1

we know that linear pair of angle is180 degrees.

angle bisector means it divides the angle into two equal angles.

so,180/2=90 degrees.

that means each angle should be 90 degree. And we  know that 90 degree is known as

right angle .hence proved.

Answer 2

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