question_answer

\[PQRS\]is a quadrilateral. \[PR\] and \[QS\] intersect each other at\[O\], In which of the following cases is PQRS a parallelogram?

A) \[\angle P={{100}^{o}},\,\,\angle Q={{80}^{o}},\,\,\angle R={{100}^{o}}\]

B)        \[\angle P={{85}^{o}},\,\,\angle Q={{85}^{o}},\,\,\angle R={{95}^{o}}\]

C)        \[PQ=7\,\,cm,\,\,QR=7\,\,cm,\,\,RS=8\,\,cm,\]\[OS=5.2\,\,cm\]

D)         \[OP=6.5\,\,cm,\,\,OQ=6.5\,\,cm,\,\,OR=5.2\,\,cm,\] \[OS=5.2\,\,cm\]

Correct Answer: A

Solution :

\[\Rightarrow \]\[\angle P=\angle R={{100}^{o}}\]and \[\angle Q=\angle S={{80}^{o}}\] Adjacent sides of a parallelogram are not equal and sum of the adjacent angles is supplementary.