For the odd angles, we use the same principle as the NAM Fractionally Angled Roads (FAR): any slope can be approximated using a fraction of "rise" vs "run". For the plain old 45° diagonal, we do something like "move 1 East, move 1 North, then repeat as far as needed". Alternately we could also go "1 West, 1 North" or "1 East, 1 South" or "1 West, 1 South". For brevity we will omit the cardinal directions and express the angles as pairs of tile movements along the latitude and longitude, e.g. 1:1 = 45°

For the FAR angles:

• 2:1 ≈ 26.565°
• 3:1 ≈ 18.435°
• 4:1 ≈ 14.036°

The general formula is tan(X degrees) - this can be entered directly into google after substituting for the angle. For example if we'd like to approximate a 20° or 70° diagonal

1/tan(20 degrees) = tan(70 degrees) ≈ 2.747 ≈ 2.75 ≈ 11:4

That is, "for every 11 tiles in one direction, move 4 tiles in the other direction". One way of laying this out would be ...

2:1 xx
3:1   xxx
2:1      xx
4:1        xxxx
...

... then repeating that pattern for as far as needed.

Other angles commonly found in regular polygons:

• Triangles, hexagons: tan(60°) = 1/tan(30°) ≈ 7:4
• Pentagons, stars: tan(72°) = 1/tan(18°) ≈ 3.08 ≈ 77:25 (aka very close to the FAR 3:1 angle of 75:25, but sprinkle in precisely two of the 4:1 segments every 25 tiles moved in the other direction to bring the ratio up to 77:25. Though in most cases it doesn't have to be that perfect, especially if kept within city boundaries)

For example, to create Captain Middle America’s shield as shown in the previous entry,

1. Starting from the middle^Note1 of a "flat" edge of the circle, this will be the "top" of the star shape, in the conventional orientation as seen in the above pic.
2. From that point, dezone a series of 3x1 tiles going in either direction
3. Then when those lines touch the edge of the circle it becomes an alternating series of 1x1 and 2x1 tiles to make the slope 2:3^Note2
4. When those lines touch the edge of the circle, connect them with a straight line, aka a road or street since this will be the only road connection to the central pentagon. Optionally, start a volcano disaster in the central pentagon to complete the vibe and to eliminate the need for a road/street running through the inside of the circle
5. Unpause to let the farms pop up, then use mayor mode trees or god mode trees (ctrl+alt+terraform in mayor mode) to fill in the dezoned tiles - might have to zoom in real close and/or hold ctrl while planting to be precise so the trees don’t leak onto the farm plots

Note1: The exact number of tiles can be counted by dragging $10/tile roads, noting the total cost, then dividing that by 10 i.e. dropping the rightmost digit. The measurement is more accurate if you pre-build the roads before measuring, because building new roads on bare terrain has an add-on cost depending on the ruggedness of the path

Note2: I actually made a mistake here, step #3 should have had twice the count of 1x1, to make the slope 3:4. I compensated for it in step #3a by nudging the straight line in #4 slightly higher