Is the OA B?

Statement 1 says that x=y. Therefore x=y=90 degrees. But this does not give us any information about the lines being parallel or not and so we cannot comment on whether a=b or not. Hence insufficient.

Statement 2 says c=x. But we know that x=A because they are opposite angles. Hence a=c and this means that both a & c are 90 degree angles. Therefore the lines have to be parallel to each other. Hence a=b because they are corresponding angles of parallel lines. Thus statement 2 is sufficient to answer the question.
Hence B.

What is the OA?
is it C?

Answer is C, why?

i think answer is C.

Reason: if x=90=y, does not tell anything but tells of a supplementary angle.
so (i) is insufficient. and if c=x=90, then definitely A=B=90. So both 1 and 2 are required to solve the problem.

Answer should be C..