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The concept of angle is a very important concept for all of Greek geometry. Many of the propositions require angles even for their statements.
The two lines are meant to emanate from the same point; two intersecting lines will actually make four angles.
The concept is also a difficult one, and, surprisingly, broader than our modern concept of angle.
As can be seen from the next definition of rectilinear angle, online math forum ; angles do not have to have straight sides; they can have curves as sides. The size of the angle does not depend on the length of the sides, but is determined only by how the two sides meet. In the Elements nearly all the angles are rectilinear, but angles with curved sides appear in proposition. continue reading on math forum.
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