You cannot, you must use a protractor.
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It is possible to construct a 20 degree angle using only Ruler and Compass. I happened to stumble across a method that is highly accurate. It is posted on my blog. Check the related link
A 10 degree angle cannot be constructed using only a compass and straight edge.
by 60 degree and 90 degree
With a straight edge and a protractor
Construct a circle and divide the circumference into 36 equal arcs Each arc will represent 10 degrees and 11 of them subtended to the circle's centre will create an obtuse angle of 110 degrees