Something I have been working with is a 32 Point Compass I have found verified lines (boulders pointing to other important spots on the 32 point compass degrees such as 112.5 degrees) as well as other degrees that are on these compass points (45 and 315 degrees are very common) so it could be worth a look. This is Not for angle/turning degrees they used 360 single degrees for that (a transit with turning degrees such as 77 degrees and 49 degrees change of direction angles) these are specifically for outright compass headings. It is worth noting that Christopher Columbus used a 32 Point Compass.
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As a side note in the book De Re Metallica the compass shown is a 24 point compass (pictured below) which is 15 degrees between each heading (instead of 11.25 Degrees like on the 32 point compass above) Another one worth checking out. I have found 75 degrees before as well as 105 degrees. If you count each one of the small lines in between there are 120 of them which are increments of 3 degrees each.
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There was a 48 Point Compass as well and is 7.5 Degrees between each point and would cover every degree I mentioned above.
The first recorded use of a 48 position mariner's compass on sea navigation was noted in a book titled “The Customs of Cambodia” by Yuan dynasty diplomat Zhou Daguan, he described his
1296 voyage from Wenzhou to Angkor Thom in detail. Advanced mariners such as Zhèng Hé used a 48-point compass as well.
One last Note: Western and Arab compasses have 32 defined points on their rose-of-winds. Eastern has 24 and 48 points.
Now how do you suppose a 24 point compass that was used in the Far East ended up in the book (De Re Metallica) A book on Mining In Europe/Germany when everybody else was using the 32 point compass in Europe at that time.
When it comes right down to it these compasses start out with 4 points N. E. S. W then divide further with 8 points, N, NE, E, SE, S, SW, W, NW, then divide equally further by 16, 24, 32, 48, 64,128 etc. all the way up to our modern degrees of 360 single degrees, which are just splitting the compass circle in halves over and over again reducing the degrees to more finite numbers (ie 360 degrees Divided by 128 degrees= 2.8125 degrees between each marked line) so the difference is you get half degrees and even quarter degrees when you divide by these other numbers which effects your readings in the field so coming up with a degree such as 112.5 in the field makes no sense on a single 360 degree compass unless you are using a 32 or 48 or above compass rose which is marked right on 112.5 degrees.