PQRS is a quadrilateral whose diagonals intersect at O. The option which will make PQRS
a parallelogram is
a. ZP + ZQ = 180°
b. ZP = 80° and ZR = 100°
c. PQ = 6.5 cm, RS = 6 cm and RQ = 6.5 cm d. PO = OR = 3 cm and SO = OQ = 4 cm
pls be precise in your ans...tks..
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Answer:
⇒ PQRS is trapezium.
⇒ SP∥RQ [ Given ]
We know, sum of two angles between parallel lines is supplementary
∴ ∠QRS+∠RSP=180
o
⇒ ∠QRS+90
o
=180
o
⇒ ∠QRS=180
o
−90
o
=90
o
⇒ ∠PQR+∠QRS+∠RSP+∠SPQ=360
o
⇒ 100
o
+90
o
+90
o
+∠SPQ=360
o
⇒ 280
o
+∠SPQ=360
o
⇒ ∠SPQ=360
o
−280
o
=80
o
∴ Measures of ∠P and ∠R are 80
o
and 90
o
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