Now that we’ve looked at a few special cases of building angles with rectangular plates, it’s time to generalize this technique. The key to this technique is to find isosceles triangle. See the following examples.

Once we’ve created an isosceles triangle, with the unique vertex having both stud and stud receive, and the other two vertices having either stud or stud receive, the angle is formed naturally. The angle formed can be calculated with this formula

Θ = 2 arctan(a/h)

a is half of the length of the unique side, and h is the height. In the example above, a is 0.5 stud and h is 4.5 studs. It’s important not to forget the 2x.

So what other isosceles triangle can we come up with? See examples below to see how we can create almost arbitrary angles.

As long as you can make isosceles triangles, you can form angles. By adjusting the length of the sides, you can create almost any angle.

## Technic Holes

You don’t necessarily need studs and stud receives to build this type of angles. You can do it with technic holes too.

## Example

See example below. The structure is complicated, but it’s based on an isosceles triangle in the end.

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