Question

prove that the bisectors of the angles of a linear pair are at right angles.
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Answer 1

Step-by-step explanation:

Given:-

∠ACD and ∠BCD are linear pairs.

CE and CF bisect ∠ACD and ∠BCD respectively.

To prove: ∠ECF=90°

Proof:-

As we know that angle on a straight line is 180°.

∴∠ACD+∠BCD=180°

⇒2∠ECD+2∠DCF=180°(∵CE and CF bisects ∠ACD and ∠BCD respectively)

⇒∠ECD+∠DCF=

2

180°

=90°

∴∠ECF=90°

Hence Proved.