Construction geometry: How to create a perpendicular plane to sketch on.

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I'm pretty sure I'm a bit stupid here, but so far I've not found a really convenient way to do the following:
Quite often I sketch an object in a sketch at an arbitrary plane (not oriented with any of the primary XY,XZ,YZ planes.)
Then I want to sketch the same thing on a plane perpendicular to that plane.
While I sometimes can use the first sketch to extrude and object, than use that object's face to create a plane to sketch on, I sometimes can't or do not want to have my sketch depend on previous geometry.
I basically want to create my own set of " X'Y' X'Z' Y'Z' " planes with X' Y' Z' being my arbitrary new coordinate system for that sketching.
What are the best/most convenient ways to construct such an auxiliary geometry?
Or, phrased differently: having a construction plane, how do I most conveniently create the two perpendicular planes to it? (Not really caring about the origin)