The answer will depend on what other information you have. If, for example, the angle is in a triangle, and you know the lengths of all three sides, you can use the cosine rule.
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Protractor
A protractor is normally used to construct angles.
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
By drawing regular polygons as for instance a square will have 4 equal right angles and an equilateral triangle will have 3 equal 60 degree angles.
Construct an equilateral triangle because each of its 3 exterior angles measures 120 degrees