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The first clue is that both of them are saying the same thing. If <QPR = 30 degrees thats the same as saying the sum of hte other two is 150. So now we are already down to either D or E.

Since both PQS and PRS are right triangles, the sum of hte other two angles = 90.
i.e. RPS + SRP = 90
and RPS + 30 + PQR = 90

This can tell you by how much PQR is smaller (30 degrees).

Q2. C

y = (x+a) (x+b)
When it intersects the x-axis, y = 0.

Therefore, x = -a or -b, and the points are (0, -a) and (0, -b).
2. Gives us (0, -6) as one answer but we still dont know the value of the other (a or b).
1. tells us the relation between a and b. Now we have all hte information needed to solve.

Heman, is there a rule that says that "The angle between OQ and + xaxis must be 60 deg". Because that i believe is an assumption.

SHA

A straight line would always have angles adding up to 180 deg
In this case I found the ange between OP and -ve x axis = 60 deg
I did not assume that the angle was 60 deg

The angle between OP and OQ = 90 deg (given in Qstem)
Hence the remaining angle ie between OQ and +ve x axis must be= 180-60-90=30 deg