Hi,
Here is a solution from a Year 6 pupil I currently teach; name of Lily Lee.
I thought that it was both beautifully simple and insightful.
The sheet has been annotated by Lily, but in short she noticed that because the circle had been, in effect, divided into 9 equal sections, then by doing 180/9 and then apportioning the result of that in the ratio of the number of dots that each angle encompassed gave her each angle, regardless of whether the triangle contained the centre dot or not.
Indeed, Lily then realised that the initial method she had developed of splitting any triangle that contained the centre dot, into 3 triangles she had already calculated the angles for, was considerably more complicated than this ultimate solution.
She is a very sharp young student, that is for sure.