Counting number of intersections for N linestrings

I have a database with D entries of polygons representing buildings. Each entry/row has the following information: id, min_height, max_height, geom (min_height is for buildings that have some kind of overpass). Details aside, I am trying to solve the following problem:

(1) Given N LineStrings (similar to lidar beams) with a shared origin and spanning 360 degrees (for simplicity you can solve the N=2 problem, i.e., two LineStrings in pointing opposite directions, or N=4 for a cross) how can I count the number of LineStrings that intersected a building geometry, hence n/N where n <= N.