To maintain tangency between a line and an edge, use the Tangent Line tool. Click on an existing edge or endpoint to start the line. It will rubber band as tangent to the selected edge and you can then indicate the length of the line. The rubber band line will not stay under the cursor, but instead, its length will be based on the cursor location, while its start and direction are controlled by the selected edge. To ensure that you are tangent to the end of an edge, select its endpoint, not the actual edge.