[Coda]

Don't worry, there is in fact a maximum angle. Your homework has an answer.

Since I'm not going to actually do your homework for you :P let me direct you to a few things that you should already know (or are at least in your book) that should help.

First, you should know the formula for static friction: F_s = μ_s * N. This means that the force of static friction equals the coefficient of static friction times the normal force. It should be noted that this is actually a MAXIMUM value, not a CONSTANT force, because friction only acts in reaction to another force.

The normal force is the force exerted on the object by the surface it's resting on. This is a consequence of Newton's Third Law, which states that every action has an equal and opposite reaction, and the object's weight applies a force on the surface due to gravity. On a level surface, this force is the object's mass times the acceleration due to gravity, but on an inclined surface, gravity doesn't point directly into it.

You should have the formulas for getting the horizontal and vertical components of a vector based on its magnitude and angle. I'll reproduce them here:
F_x = cos(a) * |F|
F_y = sin(a) * |F|
Where |F| is the magnitude of the force (mass times acceleration, remember) and a is the angle of that force relative to the surface you're considering. And remember that arcsin and arccos are the inverse operations of sin and cos, respectively.

When you're setting up these kinda of problems, it helps to draw a diagram. Draw the slope, draw the box on the slope, draw the perpendicular and parallel force vectors acting on the box, and identify which of those is equal to the normal force. Then reason about the force of friction -- if the assertion is that the box isn't sliding, then that means that the net force on the box must be zero. So look at what the force vector for friction would have to be in order to cancel out the remaining forces on the box.

With this diagram, then, you should be able to set up an equation that sets the force of friction equal to some other force, and then you solve that for the angle.

That said: This PARTICULAR one can be solved without having to actually do any math, because the coefficient is 1.0, so there's an insight that can give you the answer by inspection if you happen to think of it. But again, because I'm not going to do your homework for you, I'll let you work through this first before I spoil the answer.