I've never worried about the angle. Carefully calculate the rise from finished floors foot to head, (this may be different from a simple measurement as one floor may not be level), divide by 7.5 inches, round up to whole numbers. Divide rise by the new whole number.This is your rise. you will have one more riser than tread as the floor top and bottom take their place.
Calculate run bottom to top. Again something may not be plumb, do your measuring level. Using the number of risers minus one divide total run this is tread length. If space is adequate, risers should be less than 7.5" Run NOT less than 10". 2 x rise + run works well at 25 the average human stride. Check local codes, and comply! Use brass stops on your framing square to lay out stringers, adjust top and bottom of stringers to allow for thickness of treads and risers so each step is equal. Subtracting from bottom riser, don,t forget the thickness of top riser. Treads should overhang risers to form a rounded nosing, as should the finish floor at top.
If the stairs are to be metal, use a board to make a pattern you can try in the opening to check yourself.
If you seem to be running out of length, a common problem you can cheat allowing the bottom treads to extend beyond the line vertical from the ceiling opening, but be sure to allow plenty of head room as one nears the bottom of the stairs. No one wants a head knocker!