Explanation:
many greetings to your teacher, there are some definitions missing.
this can only be done if JM and LH are true diameters of the circle.
1. if LH is a diameter, then angles KAH + LAK = 180°.
KAH = 90° (right angle).
so,
angle LAK = 180 - 90 = 90°.
2.
with JM and LH being diameters, JAH = LAM = 42°.
JAH + JAK = 90°.
angle JAK = 90 - 42 = 48°.
3. angle LAJ = LAK + JAK = 90 + 48 = 138°.
4. see also 2.
these are angles of intersecting lines (diameters). they must be the same on both sides of such an intersected line (just left-right mirrored).
JAH = LAM = 42°.
5. angle KAM = LAK + LAM = 90 + 42 = 132°.
6. arc angle LK = angle LAK = 90°.
7. arc angle JK = angle JAK = 48°.
8. arc angle LMG = angle LAG = 180 - HAG =
= 180 - 30 = 150°.
9. arc angle JH = angle JAH = 42°.
10. arc angle KLM = angle KAM = 132°.