I am adding wood paneling to the wall, as you can see above. Starting with the next panel in the coming row I will need to cut the left end to fit the angle of the ceiling. How to I determine the angle I need to set my miter saw to?
A sliding bevel, which is a fairly low-cost tool designed for exactly this type of job - the blade can be set to match an unknown angle and locked, then it can either be measured, or used directly in setting, or used to draw a line.
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Or, a piece of cardboard or stiff paper (fold or cut to match the angle of the ceiling - set saw to match.)
In addition to the two previous answers (which can be used on the same project; some boards are easier with one method or the other), I'd like to point out another idea that is good for especially tricky spots or boosting confidence. Even when well-practised, there will be cuts you do not want to mess up or extreme cases like a brick fireplace surround.
Use paper to cut a template. Spread it out and smooth it and fold it in place. Add painter's tape to join, stiffen, or produce a cleaner straight edge.
Prototype the cut using cardboard. It's easy to cut so it's not more work, and I've used the box that the boards came in as a source!
FWIW, I have a continuous rule of floorboards on the entire upstairs with no thresholds or breaks in the pattern, even around doors into closets. A couple of rows go from one bedroom down the hall through another bedroom, the entire length of the house with a laser-straight joint.
The angle blade thing can be a lot cheaper and plainer than the one pictured. Like two bucks at the Home Depot, plastic handle with a protruding wingnut. I have two cheap ones and a nice rosewood/brass one from Lee Valley Tools' Verritas brand.
Another tip: put painter's tape on the wood board in the approximate place of the mark, then draw on that with a nice Sharpie or Black Beauty pencil. The overlap-row idea can sometimes work flipped over, and is excellent for slicing the last row down lengthwise to meet the wall (which is never straight when measured down to a quarter-inch tolerance).