Find the measures of the arcs:
7x + 8x + 12x + 9x = 360
36x = 360
x = 10
arc BC = 70°
arc CD = 80°
arc AD = 120°
arc AB = 90°

label these arcs on the diagram

m<1= 1/2 arc
        = 1/2 (80)
 = 40°

<2 is an inscribed angle

m<2 = 1/2 arc
           = 1/2 (120)
  = 60°

<3 is an inscribed angle

m<3= 1/2 arc
        = 1/2 (70)
 = 35°

<4 is formed inside the circle by two intersecting chords.
m<4 = 1/2 (sum of arcs)
 = 1/2 (90+80)
= 1/2 (170)
= 85°
Also m<6 = 85° since it is a
vertical angle with <4

<5 is formed inside the circle by two intersecting chords
OR <5 and <4 form a straight angle (line)
m<5 = 180 - 85
= 95°
Also m<7 = 95° since it is a
vertical angle with <5

<8 = a "tricky" angle since it does not FIT any of the circle angle formulas.
There are several strategies to arrive at this answer.
Inscribed <BCA is adjacent to <8 and its size is 45°.  This means <8 must be 135º to form a straight <.
OR
Once you know <6, <9, and <10, you can find <8 by remembering that the angles in a quadrilateral add to 360°.

<9 is formed by a tangent and chord

m<9 = 1/2 arc
= 1/2 (150)
= 75°
Did you use the ENTIRE intercepted arc from B to D?

<10 is formed outside by a tangent and secant

m<10 = 1/2(difference of arcs)
= 1/2 (210 - 80)
= 1/2 (130)
= 65°
Were you careful to use ALL of arc BAD?

<11 = a "tricky" angle since it does not FIT any of the circle angle formulas.
<11 is adjacent to <10 and together they form a straight angle (line).
m<11 = 180 - 65
= 115°

<12 is formed outside by a tangent and secant

m<12 = 1/2(difference of arcs)
= 1/2 (120 - 80)
= 1/2 (40)
= 20°