Unless otherwise stated, we dont know if a and b are 90 deg or less or more...
1) not sufficient... a = b could be 50 or 60 or 90 deg etc... not sufficient.
2) OP = 1/2 OQ = 4, from that we know that b = 90, but dont know the value of a. not sufficient.
combining both we know that MP is straight line and a and b = 90, so MP = 8. Answer is C.
why do you assume because OP is half of OQ, that MP is perpendicular to OQ? Can it not just be drawn from point P which is the midpoint of OQ, and perhaps joining NL with point M somewhere closer to N. It wouldn't contradict the statement 1, as a and b can still be considered vertical angles since we know NL and OQ are parallel.