Find the angle between the angle bisectors of the angles in a linear pair
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Answered by
32
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.
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Hope this will help you..
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..
Answered by
8
ANSWER: 90 degrees
Hope this helps you.
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