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I'm pretty sure this isn't an InDesign feature. In Illustrator, you can set the Constrain Angle in General Preferences which does what you want.
If you had a lot of objects like this, it might make sense to do them in Illustrator.
Thanks Steve, just making sure.
I was wondering if I'd overlooked something, because we do have a
"redefine scaling as 100%", so I though maybe there's a "redefine
rotation as 0 degrees" somewhere.
Draw a very small object on top and call upon the Pathfinder to join them. InDesign will consider the newly-wed objects to be a total new one.
A bit clumsy tho' ...
Ah, that's quite clever! To amplify a little:
1. draw another object elsewhere on the page.
2. select both objects.
3. apply the the Add option from the pathfinder options.
4. draw a marquee round the object in (1) above with the white arrow
tool to select all the object's points.
5. press delete.
6. voila: the original object remains, with the rotation set to zero!
Good one, Jongware!
I wonder if it's scriptable? The two potential problems I envisage are
whether it's possible to apply pathfinder operations with scripting
(should be simple to find that one out; I expect it is possible), and if
it is possible, would it be possible to keep track of all the points on
the added object after applying the pathfinder operation, so that they
can be deleted afterwards?
It's clever, and probably useful for a small number of objects.
The Illustrator method is much easier and a better choice when you need a large number of elements constrained to a single angle.
Although I marked Jongware's answer as correct (as it does what I asked for specifically), in fact in many cases it won't work, as far as I can tell. Using the pathfinder functions can in different/more complicated cases lead to the original graphic changing shape.