Question

please can anyone answer my question and find x and y

Answer 1

1) AB parallel to CD
so,
angle ABC = angle BCD =55°

we know from property of circle
2× angle BCD = ange BOD = x
x = 55° ×2 = 110°

ABCT is quadirateral
so,
sum of all angle = 360°
but BT and DT is tangents of circle
so, two angle 90° of quadrilateral

now, x + y + 90 + 90 = 360
110° + y = 180°
y = 70°

2) ABC is right angle ∆
so, 34° + x + 90° = 180°

x = 90° -34° = 56°

also CQ is the tangent to the circle so ,
ACQ is right angle ∆

34° + y + 90 = 180°

y = 56°

3) ABC is right angle ∆
so,
x + y + 90° = 180°

x + y = 90° ------(1)

AC parallel to ZO line
so,
x = 40°

put this equation (1)
so, y = 50°

Answer 2

3.
if any triangle on diameter 3rd point 90°
B=90° sum of angle is 180°
y+55°+90°=180°
y=35°
angle of KCD=X
D=90°
K=40°; 90°+40°+X=180°
X=50°