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Granirdred Granirdred Dec 14, 2020

PQRS is a rectangle, ∠POQ=112⁰, find angles , ​

answers: 1
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Answer:

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Here, PQRS is a rectangle.

As we know in rectangle both the diagonals are equal.

⇒ PR=QS

Also diagonals bisect each other.

⇒ PO=QO

⇒ ∠OPQ=∠PQO [ Base angles of an equal sides are also equal ]

⇒ ∠OPQ=24

o

[ Given ]

∴ ∠PQO=24

o

In △PQO,

⇒ ∠OPQ+∠PQO+∠QOP=180

o

⇒ 24

o

+24

o

+x=180

o

⇒ 48

o

+x=180

o

∴ x=132

o

Since, PQRS is a rectangle, PQ∥SR and PR is a transversal.

⇒ ∠QPR=∠SRP [ Alternate angles ]

therefore ∠SRP=24

o

⇒ ∠SRP+∠PRQ=90

o

[ Angle of an rectangle ]

⇒ 24

o

+y=90

o

∴ y=66

o

275
Dumais Roger Dumais Roger
Dec 14, 2020
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