in a parallelogram PQRS p=45°. find the value of the other angles.( apply parallelogram property)
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Answer:
325°
Step-by-step explanation:
PQRS is a parallelogram.
PO is angle bisector of ∠P
∴ ∠SPO=∠OPQ --- ( 1 )
QO is an angle bisector of ∠Q
∴ ∠RQO=∠OQP ---- ( 2 )
∴ PS∥QR
⇒ ∠SPQ+∠PQR=180
o
[ Sum of adjacent angles are supplementary ]
⇒ ∠SPO+∠OPQ+∠OQP+∠OQR=180
o
⇒ 2∠OPQ+2∠OQP=180
o
[ From ( 1 ) and ( 2 ) ]
⇒ ∠OPQ+∠OQP=90
o
---- ( 3 )
Now, in △POQ,
⇒ ∠OPQ+∠OQP+∠POQ=180
o
.
⇒ 90
o
+∠POQ=180
o
[ From ( 3 ) ]
⇒ ∠POQ=90
o
.
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Answer:
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