Explanation:
1.
central (arc) angle is twice the inscribed angle (at the arc).
127° = 2A
angle A = 127/2 = 63.5°
2.
the full circle are 360°.
127° are arc angle CT, that leaves
360 - 127 = 233° for the arc angle C A T.
3.
the central angle at O opposite of the indicated 96° angle is (due to the rules of intersecting lines) also 96°.
the triangle M-O-A is an isoceles triangle (because both legs are a radius of the circle).
that makes angles A and M equally sized.
as the sum of all angles in a triangle is always 180°,
angle A = angle M = (180 - 96)/2 = 84/2 = 42°
4. see 3.
5.
the sum of all angles around one point on one side of a line is also always 180° (they represent a half-circle).
so, the top and the bottom angle at O are supplementary to the 96° angle (together they have 180°).
so, each is 180 - 96 = 84°
that means
arc angle M N A = 84 + 96 + 84 = 264°
6.
arc angle A F = 95°
arc angle A N = 103°
therefore, arc angle F N = 360 - 103 - 95 = 162°
as explained in 1.
angle A = arc angle F N/2 = 162/2 = 81°
7.
the triangles J-E-N and J-A-N have the same inscribed angle at the arc.
angle A = angle E (I cannot read the number at E).
8.
arc angle J A N + arc angle JN = 360
arc angle J N = 2× angle E
arc angle J A N = 360 - 2× angle E (again the number there is unreadable to me).
9.
again the inscribed angle at the arc is half of the opposite arc angle.
angle Y = arc angle T A / 2 = 70/2 = 35°.
10.
we have the arc angles S Y (134°) and T A (70°).
the 2 missing arc angles to make the whole circle are equally large due to T S and A T being equally long.
so,
arc angle S T = (360 - 134 - 70)/2 = 156/2 = 78°