You can construct the equilateral triangle below (with perfect 60 angles) without using a protractor.
In plain terms:
In this worked example, the initial line is drawn using a ruler to an exact length. In this case the line is 6cm long. I now need to draw two small arcs using a compass set to the same distance (of 6cm). From one end of the line I will draw a small arc in the the top middle region above the line. I will then draw another small arc but this time from the other end of the line to the same [top middle] region above the line. This will create an intersect point from where I can draw two more lines to each end of the first line that I drew. This triangle has three perfect 60 internal angles and each side is of equal length to the others thus making it an equilateral triangle. You can bisect one of the angles to make a 30 angle.
(Take a look at the dotted lines that represent the path of the compass. Note that I am not drawing the entire path of the dotted line. I am drawing the two small arcs only. Don't forget that if you are asked to construct a triangle in this way then ensure that you do not erase the arcs as this is evidence of your work.)
Run the graphic below to watch how to construct this equilateral triangle.