Darkness has descended on the infinite plane of Euclidea. The only sources of light are $4$ lighthouses; they were built long ago, and cannot be moved. The bulbs of these lighthouses can be rotated any direction, and illuminate a $90^\circ$ sector of the plane. The Euclideans want to bring light to the entire plane: can they do it, no matter where the lighthouses were built?

What about when there are $5$ lighthouses, but they only illuminate a $72^\circ$ sector?

(Think of the light houses as being transparant, they don't cast a shadow).

**Edit** Statement was reworded to clarify that the lighthouse locations cannot be chosen.