you might not be able to construct all the angles, but using a compass you can construct some angles by constructing angular bisectors.
eg:construct angular bisector of straight line i.e; 180 degrees it gives 90 degrees
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A protractor is normally used to construct angles.
Construct an equilateral triangle because each of its 3 exterior angles measures 120 degrees
Protractor
With a straight edge and a protractor
You cannot, you must use a protractor.