Question

What is the measure of angle between the bisector of adjacent angle in linear pair?

Answer 1

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Answer 2

The angle between the angle bisectors of the angles in a linear pair is 90°

Proof:

∠ACD & ∠BCD form a linear pair

∠ACD + ∠BCD=180º

∠ACD/2 + ∠BCD/2 = 180º/2

[ Divide by 2 on both sides]

∠ECD + ∠DCF = 90º

[ CE and CF bisect ∠ACD and ∠BCD ]

∠ECF = 90º

[∠ECD + ∠DCF = ∠ECF]

∠ECF is the angle between CE and CF which bisect the linear pair of angles ∠ACD and ∠BCD.

Hence, proved that the angle bisector of a linear pair are at right angles to each other.