I have severe water damage to the drywall at the two lower corners of an upstairs window due to leaky outside seals. I'd like to repair this damage in conjunction with replacing the window. However, I've never repaired this type of an area before since it involves 90 degree angles at the corner of a window. Should I make an L-shaped patch which extends to the floor? Any suggestions on an approach would be most helpful

 

Yes, you want to avoid having a seam that aligns with the opening. Cut the old back to a point that it is solid and is over a stud for nailing or add stud material to the side of an existing stud for nailing. Using mesh drywall tape eliminates the step of having to bed the paper tape into the joint compound.

Hope this helps.