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Woodworking can sometimes seem like a geometry exercise. It’s not just the wood - woodworkers often talk about angles in their tools. Those angles then combine to create new angles….
I’ve heard people complain of "the tyranny of right angles", but in joinery, right angles are popular because they simplify design of both tools and pieces. You won’t always been aiming for 90 degree joints, but it’s very common. 180 degrees, of course, brings you to flat and 360 is a complete circle.
Figure showing 90, 180, and 360 at work in a case.
After 90, the most commonly targeted angle is 45, which is half of a right angle. Miters, like the angled corners on picture frames, are 45 degree angles. If you want to make octagons, the 45 gets split again into a pair of 22.5 degree angles. Though 30 and 60 degree angles are common in drafting triangles, they’re unusual in wood.
Carpenters, framers, and roof-builders go much deeper into angles. The normal angle for cutting crown molding, for example, combines 33.85 degree angle with a 31.6 degree angle. You’ll see these angles marked on some tools, but shouldn’t need to use them for making furniture. (Unless you get really wild with the moldings…)
82 degrees. Why would someone want a tool at 82 degrees? And why does it seem like everything gets sharpened at different angles?
10-15 - knives and some carving tools (12 bed for many bevel-up planes) 20-30 - chisels, plane blades, carving gouges 35 - mortise chisels and similar 45 - axes, parting tools (standard plane frog) 50 - turning gouges 70 - turning scrapers 82 - countersinks (to match screw heads) 90 - hand (card) scrapers