This seems like something a Python script could handle, but I have not been able to find any. The maths is not all that difficult. Perhaps you would have better luck finding one.
There is a kludgy workaround. Essentially you want to extend both edges all while keeping one end fixed.
Press the . (period, full-stop) key to make rotation and scaling occur around the cursor.
In Edit mode, select the fixed-end vertex of edge 1. Snap the cursor to this vertex with Shift-S.
Shift-select the vertex at the other end, use S-key to scale the edge. Scale to about where you think the lines will intersect.
Note: If you do not want to deform the mesh, you will have to create a new edge on top of the original.
Repeat for edge 2.
Now the kludgy part; you’ll have to zoom in and continue the scaling procedure. Fiddle with the endpoints until they overlap (use N key to watch coordinates in the Transform window).
When you are satisfied, select both endpoints and Alt-M to merge them at the intersection.
If anyone has an easier, more accurate way to do this (eg has actually taken Descriptive Geometry) please let us know.