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Use a set square? (Or 2)
https://www.screwfix.com/p/dewalt-rafter-square-7-177mm-/780ky -
Could you drill a hole on one wall where you want the pole to be, then fix your lazer to the hole and pew-pew it to the other wall?
I guess the risk is your lazer might not be fitted straight.
If your walls aren't perfectly true there's a good chance that doing by eye will end up looking straighter anyway. I remember as a teenager spending ages mounting an acrylic sign perfectly level only for it to look wonky and shit because it was an old house and nothing was straight. Did it by eye and it looked perfect.
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perpendicular to both walls and level
The problem you will have is neither wall is likely to be particularly square/straight or parallel to the other. Get it level (using a level) and as square as you can (by eye or using a square if you want to measure how far out it is), which will mean it's slightly off square at both ends but no one will ever come and check the angle but you will see it every day.
Where is the door to the room, this is where you will look at it from mostly, and where will you be when hanging stuff up? Figure out where you will look at it from and do the best you can.
I am fitting a pole in a small utility room, to hang wet washing off and the like.
I need the pole to span from wall to all at exactly 90 to ensure it is the right length and that it lands correctly in the wall fittings.
I have a lazer level which will make sure it is vertically level, but trying to find a way to make the pole perpendicular to both walls and level is thrashing my head.
Anyone got any pro tips?