Page "Angle trisection" Paragraph 37

Then, the markedness of the ruler comes into play: it is " anchored " at point A, and slided and rotated until one mark is at point C, and one at point D, i. e., CD = AB.

A radius BC is drawn as obvious.

That is to say, line segments AB, BC, and CD all have equal length.

( Segment AC is irrelevant.

) Now, Triangles ABC and BCD are isosceles, thus ( by Fact 3 above ) each has two equal angles.