If the slope is the same between two intersecting roofs, the angle of the valley is 45 degrees.
If they’re different, you can figure it out graphically. Draw a side elevation of the house, showing the main roof on edge with the dormer roof intersecting it.
Measure the length of the lines you drew for the peak of the dormer and the eave.
Transfer these measurements onto the subroof.
Of course, you’ll have the width of the subroof from your front view, or elevation.
If this were a bigger dormer, I would have done the math. Here I ended up using a little trial and error until I got an angle that was close. I kept trimming sharper angles of a paper template. Then I glued on the roof and sanded the whole component with a circle motion until I got it to lay flat. It was very easy.
I bet you I’ll need suggestions on the backyard bay window, when I get to it.
I know the fine folks at RMWeb will probably hunt me down and tar & feather me, but why are you calling that a “Country” house?
In the US, it would be know as a suburban home, and not a very impressive one either (not even close to McMansion level). Aren’t there homes like that in London suburbs? Not everyone lives in a terrace, a tower block, or a council estate.
I have more pictures from the client which shows the entire 6 acre lot. It is all in the country, and her filename has a UK prefix. So, I call it a UK Country House.
I sold roofing for most of my career (as well as other stuff but roofing was the bulk of my business). I remember the very first day I was being trained. I looked at dormers and didn’t have a clue as to how to figure them out. It took my trainer Roger just a few minutes to explain how simple the math was.
I can’t prove this of course, but I was actually thinking what if they meant UK as in Kentucky, and not Great Britain? The reason why is that big houses in Britain seem to be either stone or some Tudor/stone hybrid, kind of like this wood-frame British house, and nothing really like the house you are recreating in scale, which seems North American in style (or perhaps…New Zealand)
That said, you seem to be off to a good start, except for those gaps in the side Fascia of the dormer - are they to be filled later?
As a born and bred resident of the United Kingdom, I may say “tarred and feathered will you be”, sir ! Glad that we have now resolved the geographical and structural discrepancy.
Aha, but as was subsequently established, that house is in Kentucky in the United States. So my original determination still stands, that is not a United Kingdom Country house, indeed although there must be some since the UK is so big, my searches turned up large wood frame houses (apparently not all that fired common to begin with) as using the Tudor Framing/Wattle & Daub* style. So, no feathers in my cap for me…
*Well, actually composite panels designed to look like Wattle & Daub.