This project add an angled corner and joists to the framing for a deck on a sloped site.
To mark the angled cut line, measure out from the corner an equal distance in both directions. Align a straight 1x4 with both measurements, and mark the header and the rim joist. Transfer the marks to the faces of the boards with a square.
Cut and install the joists with the crowns up. Attach joist hangers at the ledger. At the header use joist hangers, or drive screws or nails through the header into the joists. To measure for cutting a joist at the angled section, hold it in place and mark it: Have a helper hold one end up against the ledger so that its bottom edge is close to the top of the ledger. While another helper measures to see that the joist is parallel with the next joist, mark the bottom of the joist. Transfer the mark to the face of the joist using a layout square, and cut at a 45-degree angle.
If a set of concrete steps is in the way, notch the joists. Cut a joist to length and hold it in place. Level the joist. Steps often slope away from the house, so there may be a gap under the joist. Mark where the joist meets the top of the ledger. Transfer that measurement to the joist where it crosses the edge of the step. Lay out your cut line between these two points.