The birdsmouth is such a simple looking cut, going into a rafter and onto a wall plate, but getting the angle and depth right is something that fools the most experienced of carpenters.
Birdsmouth cut in position on top of wall
The diagrams above show a roof pitched at 30 degrees. The same method will apply for other angles.
Cut the top of the rafter at 60 degrees. Then lay the rafter in position on the wall plate.
Next, mark the point where the rafter touches the wall plate and mark this point, point A. Mark line 1, which is from point A at 90 degrees across the rafter.
Then mark point B, at whatever depth you need, up line 1. Then draw line 2 at 90 degrees to line 1. The top of the birdsmouth cut can then be drawn.
In this example it is 30 degrees down from line 2. The other (front) cut line of the birdsmouth is drawn at 90 degrees to that. The angles can be found and marked using a Set square, a Sliding bevel and an angle finder. All are shown in the top tools box.