Explanation:
by the way, you are completely and exactly right at 6.
Q is the inscribed angle of the (inner) arc angle TR.
and as such it is half of that arc angle TR.
S is now on the same side of the circle center as the segment TR. so, we have to flip the situation around :
S is half of the outside arc angle between T and R.
as the sum of the inner and outside arc angles are 360° (the full circle), the sum of half of their values is then
360/2 = 180°
so, yes,
x + 2 + 9x - 7 = 180
10x - 5 = 180
10x = 185
x = 18.5
Q = x + 2 = 18.5 + 2 = 20.5°
S = 9x - 7 = 9×18.5 - 7 = 166.5 - 7 = 159.5°