We have a sphere here being held up at two points on two planes. Since they are planes, the forces can only act normal to the planes themselves. This already gives us the directions that the forces act, but not the magnitudes. The thin black lines through A and B show the direction that the normal forces (solid green) can act in. (The x and y components of the normal force at B are the dotted green lines).
The weight of the sphere (blue arrow) is the only force that has to be taken care of by the two normal forces. The fact that point A is on a vertical plane and using what we just showed above, it is clear that point A cannot support any of the weight of the sphere. Therefore we know that point B supports all of the weight of the sphere (so the y component of the normal force at B is the weight of the sphere mg). But since point B is on an angled plane, there will be a component of the normal force in the x direction as well. We know the y component of the force and the angle, so we can find the resultant total force.
Now that we know the total normal force at B, we move on to A. We need equilibrium to assure that there is no movement in the system, but as you can see, there is a horizontal component of the force at B which must be compensated for by A. For the sum of the forces to equal zero, the force at A must equal the horizontal component of the normal force at B.
As a quick check, we can make sure that adding up the force arrows brings us back to the same point.
They do add up to zero, so the answer checks.