An obtuse dovetail is a joint where the angle between the two parts is greater than ninety degrees (and less than one hundred and eighty degrees). In this example, the angle will be one hundred and ten degrees, but no math is used, so the method will work with any obtuse angle.

It's a little more complicated than a standard dovetail, which is at ninety degrees, but follow carefully and you'll be able to manage it.

As usual, I've filmed a video of the process for greater clarity:

Step 1: Marking for the Tail

Yes there's a lot of photos! I've tried to show every step, since this is the most crucial stage

I'm using parts which are the same width, but different thicknesses

Use a dovetail marking gauge (https://www.etsy.com/uk/listing/288703591/dovetail-marking-gauge-mp168-limited) to mark the slopes of the inside tail (the side that faces the obtuse angle, and won't be seen when the joint is assembled)

Mark the angle, at the end of the other part, to find the finished length across it. Use a bevel gauge set to the desired angle to one end of it's blade (this automatically sets the other end to 180 minus this angle)

Use this finished length, to mark off how far the dovetail slopes need to extend, and use a marking gauge to scribe a shoulder line for it

Using the same bevel gauge, scribe the shoulder line across the sides of the tail piece, and also at the end

Reset the marking gauge and scribe the shoulder line on the reverse face of the tail piece

Scribe a line to define the waste portion at the end

Now use a try-square to transpose the corners of the dovetail from the inside surface to the outside surface. You're recreating the same shape, but it's shifted back from the end, due to the joint angle

Join the corners up, extending the slope lines to the end of the piece

Now on the end, join the two dovetails together with lines. These should diverge from the smaller, inside dovetail, to the extended, outside one

Step 2: Cut the Tail

Saw down the dovetail slopes, following the diverging lines on the end

Now saw off the end waste

Finally saw in the dovetail shoulders

The resulting dovetail is quite distinctive, and you should find that the end is now rectangular

Step 3: Marking for the Pins

Saw off the angled end of the pin board, which was marked during marking out for the tails

Rest the tail on the end of the pin board, and mark the dovetail slopes

Mark in perpendicular lines for the pin sides. This can be tricky since the end is angled, and you can use a marking gauge to check these are parallel to the board's edge

Mark in the length of the pins, directly from the tail piece, and use a try square to scribe the base of the pin socket