Question

If OP,OR,OQandOS meet at point O.then prove that anglePOS+angleROS+angleQOR+anglePOQ=360degree​

Answer 1

Explanation:

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In figure OP,OQ,OR and OS are four rays. Prove that ∠POQ+∠QOR+∠SOR+∠POS=360

o

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Answer

Let extend ray OQ backwards till T

⇒ Now, ∠TOP+∠POQ=180

o

[ Linear pair ] --- ( 1 )

⇒ ∠TOS+∠SOR+∠QOR=180

o

[ Linear pair ] ----- ( 2 )

Adding equation ( 1 ) and ( 2 ),

⇒ ∠TOP+∠POQ+∠TOS+∠SOR+∠QOR=360

o

Since, ∠TOP+∠TOS=∠POS

∴ ∠POQ+∠OR+∠SOR+∠POS=360

o

--- Hence proved

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