The number of angles in Fig. 2.8 is

There are 3 individual angles

Then 2 angles in pair of 2, i.e., 40+20 and 20+30 (40+30 is not considered as it is not continuous)

And then there is one angle which is the pair of all three i.e., 40+20+30.

So in total there are 6 different angles.