A generalization of Morley's theorem can be obtained by considering external angles (supplementary angles of the interior angles) of the triangle. Taking certain intersections between angle trisectors of the external angles and the ones considered earlier we can get four equilateral triangles, as can be seen in the applet below. In it, the gray triangle is the initial triangle, the angle trisectors of its internal angles are shown in green, the angle trisectors of its external angles are shown in red, Morley's triangle is represented in green and the new equilateral triangles are represented in yellow. Note that the sides of the central yellow triangle are in the extension of the sides of the other three yellow triangles, so these have the sides parallel to each other (and parallel to the sides of the green triangle).

(Click on the points \(A\), \(B\) and \(C\) to change the shape of the initial triangle)