I am installing 2 1/2-inch hardwood strip flooring in a hallway. The hallway takes a 90-degree turn at the point where the addition meets the original structure. The twist is that it makes this turn by combining two 135-degree angles, as is depicted in the accompanying image. [For some reason I'm unable to upload the image.] I want the flooring to be parallel to the walls for the entire length of the hallway on either side of the angle. The floor joists aren't a factor because they take a 90-degree turn at the angle. I'm thinking of mitering the ends of the strips at the angles, and perhaps inserting a perpendicular strip between the mitered ends as a sort of transition piece. Thoughts? Suggestions?