Question

PORS is a rectangle. Find angle OPS, us given
angle QOR is
given,where O is 56°​

Answer 1

Answer:

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Step-by-step explanation:

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