How to make angled walls without overlapping?

I’m trying to end a hallway in an octogon shape but no matter how perfectly I try to line up the walls, the corners of them are always sticking out and clipping through. How can I prevent this?

The other comment below yours describes the ideal solution.
Another functional but worse solution you should be aware of is vertex snapping:

  1. Select the angled wall.
  2. Hold V and hover over the vertex you wish to use for the pivot point.
  3. Drag the new pivot point onto the corner of the other mesh you want to snap to.

That way you can snap the very top or bottom corner of one wall to another perfectly.