Expert: Dan Griffin - 3/27/2009

Question
How do I figure the angles and cuts to make a peaked roofed?

Answer
Josh, there are entire textbooks written to answer this question.  I suspect you've not made much effort at research.  There is no simple answer.  This fella actually has a very good discussion and lessons that cover far more than I would be willing to write:

http://www.carpentry-pro-framer.com/

The rules for this are the same whether it is a mansion, a shed in the back yard,  or a dog house.
Pitch determines the angles.  How steep is the roof?
Pitch is a relationship between rise and run most often expressed as inches per foot.  A very common easy pitch is 4 in 12, meaning that for every 1 foot that the rafter travels in the horizontal, it rises 4".
The length of the rafter is determined by the width of the building also known as span.  A building that is 20' from outside to outside needs 2 rafters that each travel 10 feet in the horizontal, because they have pitch the rafters need to be longer than 10'.  Each foot of 4-12 pitch requires 12.65".  There is a scale on a good framing that gives this number under the 4 on the length of common rafter scale and there are several other methods of deriving the length of the rafter.  Add whatever eave overhang you desire, make an allowance for the ridge if used.  The actual angle can be drawn on the board with either a speed square or rafter square.

Look over the web site I gave you, if you have more questions you now have a bit more information and some of the proper terms to use.