Since it's still early, I'd like to expand one the method of using slope ratios to develop the angles needed for half-lap rafter peaks. Using Don P's drawing as the visual reference, let's describe the situation from the point of reference of the peak intersection, the rafters descend from the peak by opposite but equal slopes, 4/12. So when we use slope in layout we are referencing from vertical and horizontal lines or planes. Keeping the drawing in mind and extending the lines of the rafters in their uncut state, draw a horizontal line through the peak and you will visually see the equal and opposite slope of the two rafters. Onto the rafter stock, let's assume the rafter seat cuts and rafter length to the peak is known and marked on the rafter stock. Go to the peak and place the framing square on the rafter with the 12 at the peak and the 4 on the down slope, mark the line from the peak across the stock. That is the level line reference for the next step. At this point you might encounter a level line is to short for using 4/12 slope, so you can use any multiple of 1/3, which is the simple root ratio, let's say 2/6 works. Hold 6 at the peak and 2 from the level line with the slope in a descending direction, mark peak to 2 inch mark. That should get you everything you need to establish the basic angles.

I hope this can be worked out from my explanation. Once you see the reasoning, one can handle the problem with carpentry layout tools without need for calculators, trig or computer design tools.

I have edited out a mistake, I am doing this without the aid of a square and a test board.