.. a tool that saves me from doing any math.

Some math, I am afraid, is inevitable...

The tool that did the math for me was FreeCAD. It has the sketcher, which allowed me to draw all walls, applied constraints like distance, angle and certain alignments. Finally it is possible to apply an angle constraint to every corner, but I used the dialog window to just peek at the calculated value.

Now with all the data, it is possible to draw a room and apply the values for length and angle of a wall, using the Enter key.

For some reason some drawn angles are slightly wrong, likely rounding errors. But in the end my figure was almost correct once I corrected the incorrectly calculated values manually, just an offset of 1cm for the last wall.