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

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The Brainliest Answer!

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.

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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

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