From The diagram in the question.
Step 1: To find M,
M + 90+ 60 = 180(sum of angle in a triangle)
M + 150= 180
M = 180 - 150
M = 30
Use similar reason,
40+ 90+N = 180
130 + N =180
Therefore, N = 50
Step; Using angle on a straight line
112 + x = 180
x = 180 - 112 = 68
Then, M + X + Y = 180
30 + 68 + Y = 180
98 + y = 180
Y = 180-98 = 82
Note that Y and X are vertically opposite angle
P = 82
Step 3 ;Find q
70 is a vetically opposite angle
p + q + 70 = 180 ( sum of angle in a triangle)
82 + q + 70 =180
152 + q = 180
q = 28
Step4 : To find T ( Note that Y is vertically opposite to T)
N + 68 + Y = 180 ( Sun of angle in a Triangle)
50 + 68+ T = 180
118 + T = 180
T = 180 - 62
T = 118
Step 5 ; Find r
using sum of angles in a triangle
90 + 50 + r = 180
140 + r = 180
r = 40
r is vertically opposite angle
r + s + 70 = 180
40 + s + 70 = 180
110 + s = 180
s = 70°
Step 6; find U
From t, using angle on a straight line
t+ a = 180 + a = 180
118 +a = 180 - 118= 62
s + 62 + v = 180
70 + 62 + v = 180
132 + v = 180
v= 48
then, V is vertically opposite
90 + u + v(vertically opposite) = 180
90 + u + 48 = 180
u = 180 - 138
u = 42°.
Therefore, M = 30°, N = 50°, p= 82°, Q= 28°, R = 40°, S =70°, T =118°, U = 42°