The correct answer is: C. Both force polygon and funicular polygon must close.
A force polygon is a graphical representation of a system of forces. The forces are represented by arrows, and the sum of the forces is represented by a closed polygon. A funicular polygon is a graphical representation of the equilibrium of a system of forces. The forces are represented by strings, and the strings are in equilibrium when they form a closed polygon.
For a non-concurrent force system to be in equilibrium, the force polygon and the funicular polygon must both close. This is because the sum of the forces must be zero, and the forces must be in equilibrium.
Option A is incorrect because the closure of the force polygon is not sufficient for equilibrium. The funicular polygon must also close.
Option B is incorrect because the closure of the funicular polygon is not sufficient for equilibrium. The force polygon must also close.
Option D is incorrect because both the force polygon and the funicular polygon must close for a non-concurrent force system to be in equilibrium.