The figure shows a regular polygon with $12$ vertices, all on one circle. Any three of the vertices form a triangle, which gives $\binom{12}{3} = 220$ triangles in all. How many of these triangles are acute-angled, that is, have all three angles less than $90^\circ$?

Fig. 1: A regular polygon with 12 vertices on a circle, shown as dots. One sample triangle joins three of the vertices and is shaded lightly; the centre of the circle is marked with a small cross.