Trisecting an angle In this Numberphile video it is stated that trisecting an angle is not possible with only a compass and a straight edge. Here's a way I came up with: > Let the top line be A and bottom line be B, and the point intersecting P. > 1\. Use the compass and pick any length. Draw a point M n units from P on A. Use the compass again to draw a point N n units from P on B. > 2\. Connect M and N. > 3\. Since we know how to trisect a line, we can trisect it and get 3 equal distance line segments with 2 points in between. > 4\. Connect the 2 points to the point P. > 5\. Done. This seems to work for all angles that are not 0 or 180 degrees. Given that it is proven that it's not possible to trisect an angle with only compass and a ruler without marks, something must have been wrong in my steps but I can't see any. Where is my mistake?

Let your angle be almost 180 degrees, so your two lines are almost coincident. The line $MN$ is also almost parallel to the lines, and trisecting that segment leads to very unequal "thirds" of the angle.