Question

Find the angle between the angle bisectors of the angles in a linear pair

Answer 1

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 bisectors of a linear pair are at right angles to each other.

==================================================================

Hope this will help you..

Answer 2

ANSWER: 90 degrees

Hope this helps you.