In a given figure AB and EF are parallel to each other.prove that CDEF is a Cyclic quadrilateral
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2
Answer:
CDEFisacyclicquadrilateral.
∠FED=80
o
(Given)
∠FED+∠FCD=180
o
...(sumofoppositeanglesofcyclicquadrilateralis180
o
)
⇒FCD=180
o
−80
o
=100
o
.
SinceAB∥CD,
⇒ABCDisaparallelogram.
∠ABC+∠BCD=180
o
...(Adjacentanglesofparallelogram.aresupplementary)
∠BCD=∠FCD=100
o
⇒∠ABC=180
o
−100
o
=80
o
∠ABC=∠FBA=80
o
.
Hence,optionCiscorrect.
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