The mathematical formula I was taught when I did my City and Guilds (centuries ago so it seems) to find out the equivalent focal length comparison was the following:-
Divide the wider angle lens focal length into the standard lens focal length, so the 65mm into the 80mm = 1.23.
Now divide the 35mm equivalent standard lens, assumed to be 50mm, by the same factor, i.e. 1.23.
This gives a result of 40.65mm which is what the equivalent focal length would be needed on 35mm.
Likewise the 55mm divided into the 80mm gives 1.45 (recurring) so dividing the 50mm by the 1.45 you get 34.48mm equivalent.
It has little to do with diagonals because of the different shape format. You only need to judge that to get approx the standard lens size needed for that particular camera, but as this is already decided for us by the manufacturer, we have no control over this.
This works for other cameras too.
A 35mm wide angle lens used with a Mamiya 645 camera using this formula gives a wide angle result of 21.88mm (22mm for all intents and purposes) equivalent on 35mm cameras
Taking another example the, Bronica ETR series and the Bronica Sq series. The standard focal length on both is 75mm. so a 45mm W/Angle on both cameras gives a factor of 1.666
Therefore the equivalent for a 35mm camera using a 50mm lens is 30mm. It is not the diagonal, it is the width of the longest side is the controlling factor.