so to solve part (a) you would set F1x=F2x
this is because in equilibrium there is no movement horizontally and vertically, and therefore these two opposing forces must be equal and opposite.
from there you can solve for theta
to solve (b) you would set F1y+F2y=mg
this is because, once again, there is no movement vertically so all the up forces must cancel out the down forces.
plugging in theta and and g will let you get an answer.