The sum of the left turns equals 360 degrees (the turtle has completely rotated around). In math terms, the sum of the external angles of a regular polygon is 360 degrees. Here, we have a 12-sided regular polygon which rotates until the image coincides with the preimage. That is 360/12 = 30 degrees (the outside angle). I think the angle is 30 degrees because the polygon has total of 360 degree then divide it to 12 then you will came up with a 30
