Explanation:
a.
the arc angle AC = 180° (since this is a diameter).
the arc angle BC = 60°.
so,
arc angle AB = arc angle AC - arc angle BC = 120°.
b.
the exterior angle of a circle segment at the circle arc is half of the interior angle at the center of the same segment.
the angle A = arc angle BC / 2 = 30°.
c.
the same principle as in b.
the angle C = arc angle AB /2 = 60°.
d.
the arc angle AD = the angle at AOD (that is how arc angles are defined).
the angle AOD = the angle AOF.
the sum of all angles in a triangle is always 180°.
angle AOD = AOF = 180 - 90 - angle A = 60°.
e.
as explained, this is the same as the arc angle AD and therefore the same as d.
it is 60°.
f.
the arc angle CE = the arc angle AD = 60°.
remember, the angles of intersecting lines are the same (just side mirrored) on both sides of each line.
g.
the arc angle ABE = arc angle AB + arc angle BC +
+ arc angle CE = 120 + 60 + 60 =
= 240°
h.
the angle AOE = the arc angle AE = the remainder of 360 minus the arc angle ABE of g.
so, angle AOE = 360 - 240 = 120°