How do ladybug wings get "packed away"?

Question

When they land their wings are sticking out of their wing covers or I call the shell. Then the wings slide in. Aren't wings sposed to be rigid for flight?

Answer 1

They are somewhat rigid and fold up when not used. When they are flying, the lifting forces unfold them, much like an umbrella.  

Answer 2

The black lines we see in the wings of all insects are actually blood veins.  The lady bug can open and close a valve to control blood flow to the veins to expand or collapse the wings.  That and muscles pull it back under the elytra. (the proper name for the "shell")