Question

Prove that the. bisector of two adjacent supplimentary angle are at right angle​

Answer 1

Answer:

To prove that the bisectors of two adjacent supplementary angles include a right angle we draw the supplementary angles and also construct the angle bisectors of both the angles. ... OD is the angle bisector of angle ∠AOC and OE is the angle bisector of ∠BOC .

Step-by-step explanation:

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Answer 2

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$\huge\red{Given:}$

• CE−→−CE→ is the bisector of ∠ACD and CF−→−CF→ is the bisector of ∠BCD

$\huge\green{To Prove:}$

• ∠ECF = 90o

$\huge\pink{Proof: }$

From the figure we know that

∠ACD and ∠BCD form a linear pair of angles

So we can write it as

• ∠ACD + ∠BCD = 180o

We can also write it as

• ∠ACE + ∠ECD + ∠DCF + ∠FCB = 180o

From the figure we also know that

• ∠ACE = ∠ECD and ∠DCF = ∠FCB

So it can be written as

• ∠ECD + ∠ECD + ∠DCF + ∠DCF = 180o

On further calculation we get

• 2 ∠ECD + 2 ∠DCF = 180o

Taking out 2 as common we get

• 2 (∠ECD + ∠DCF) = 180o

By division we get

• (∠ECD + ∠DCF) = 180/2
• ∠ECD + ∠DCF = 90o

Therefore, it is proved that ∠ECF = 90o