AngleMultiple

To produce multiples of angles:

1) Create an angle <(EFG) .
2) Create a number object : type a number f (e.g. 2.0) and press the enter key.
3) Get the multiplication tool (*) from the toolbar on the right side.
4) Click on the number object and the angle <(EFG).
5) This creates an angle <(EFH), whose measure is f times the measure of <(EFG).
There is a problem though, due to the way angles are measured.
The tool [Measures \ Angle Label], used to measure angles has a restriction.
It produces measures in the interval (-pi, pi). And this fails to give correct results for multiples of angles. Try it in the following example. There the number-object "Quot" gives the quotient of the two angles : <(EFH) / <(EFG) = f. This is correct only when both angles are less than 180:00.
The angle <(EFH) is indeed the correct multiple of <(EFG), but the Angle-Labels may be wrong.
To cure that a variation of the tool is needed that works with angles greater than pi.
See below how this tool can be applied.

Correct display of the multiples of an angle.

Do exactly the same actions as before. But when clicking on the angles with the [Angle-Label] tool, to get their measure, press simultaneously the ctrl-key. This makes the measurement-tool work with the continuous angle-mesure, which can take any real number (or degree) as its value. Catch and rotate "C" about "B" below, to see what I mean.
The angles can become arbitrary large, but their ratio remains fixed.

http://users.math.uoc.gr/~pamfilos/