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I agree that you should not read the angle from the Properties palette and then type it in. You may have your precision of angle display rounded off to the nearest whole degree, and that will not often be the actual angle. But if that's the issue, I wouldn't expect your results to be off by more than half a degree, not the 2 degrees you describe. Do you have some object snap mode(s) running that could throw things off?
You can align your crosshairs direction with the direction of anything, using AlignSnap.lsp, with its AS and ASB commands, available >here<. And not just straight things with linearity like Lines and Polylines, but Text or Block rotation angles, curves at the tangent direction at the pick point, etc. Then with Ortho on, what you draw will be parallel [or perpendicular] to it, regardless of angle display precision in Properties. The AS command aligns the direction only; the ASB command also puts the Snap Base at a logical location in relation to the picked object. See the comments in that thread and in the code.
You could also just COPY the "source" object, and edit the copy in various ways, for length, and/or Layer, and/or whatever other aspects you need.