Bastard mitre joints
Bastard mitre joints are ones where the overall joint angle is not 90 degrees. You may encounter these in a number of circumstances, and without the aid of angle finding tools or at least a sliding bevel gauge they can be difficult to cut accurately. However there is a simple way to lay out these cuts in some circumstances, and all you need is a pencil and a straight edge.
The Bastard Mitre
This article describes how to mark out and cut a bastard mitre without the need for any angle finding gauges or tools.
Let's say we want to fit the architrave to an odd shaped door opening - perhaps like that you would find into an eves cupboard in the loft space of a house:
The very acute angle here will require a bastard mitre to be cut at the top for the two sections of architrave to meet neatly.
Start by offering up the first architrave and allowing it to sail past the final position:
Now draw along both sides of the timber:
Now position the second timber in its intended position:
And draw the lines for that one:
Finally using a straight edge, draw a line between the points of the parallelogram that you have now marked:
Note you need to draw past the ends of the parallelogram to make the nest step easier. Lay you timber in position, and place the straight edge on top. Align the ends of the straight edge with your lines. Use this to mark the timber:
Repeat for the other bit of wood, and cut along your lines. The result should be a perfect bastard mitre: