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:::I'm not saying the concept of unsigned and unoriented "angle" doesn't have a place, but I looked and there aren't any obvious references that argue against the signed definition. So the relationship I infer from the sources is signed as canonical and unsigned as a simplification, rather than the unsigned being canonical. I guess we could call the small angles "reference angles" (0-90 degrees) or "proper angles" (0-180).
:::I'm not sure what your point is with spherical trigonometry, the angles are still rotations and the sets of rotations around a point forms a circle group. The fact that the rotations form SO(3) and can be labelled with dihedral angles or 3D bivectors is interesting but not really relevant to defining angles.
:::As far as writing for a non-technical audience, [[WP:TECHNICAL]] is of course the guide. But notably there is [[WP:OVERSIMPLIFY]]: "Encyclopedia articles should not 'tell lies to children'". So dumbing down the definition of angle is not the right approach. I would say the lead paragraph should give a good definition in terms of the circle group and define general concepts, and then a second paragraph can then go on to describe common examples. Lie groups are relevant to defining angles in higher dimensions, but the basic notion of angle is defined in a plane, so the Lie groups can go in a section. [[User:Mathnerd314159|Mathnerd314159]] ([[User talk:Mathnerd314159|talk]]) 18:33, 5 May 2023 (UTC)
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