Question

o is the centre of the circle.find size of unknown angle

Answer 1

8) x = y = 45°

9) x = 90-40= 50°

y = 50×1/2= 25°

z = y = 25°

10) x = 35°

y = 55°

Answer 2

In question number 8)- The angle x and y are given equal. The thrird angle is 90° as it is the tangential angle (tangential angle is always 90°). Thus x+y+90° = 180°
2x= 90°
x=45°
and y=x
So y=45°

In ques 2
In the triangle (45° and x) the third angle is 90°(tangential angle)
so x+40°+90°=180°
so
x=50°
Angle y and z are equal(as they both originate from the circumference and both end at the centre)Let the third angle be a.
Now x+a must be equal to 180°( straight line)
therefore
a=180°- 50°
a=130°
y+z+a=180°
2y=50°
y=25°
z=25°

Ques3)-It is a cyclic quadrilateral and each side is equal to 90° (360°/4)
Thus y+35°=90°
y=55°

Let the top angle be 'a'
a must be 90° (angle suspended by the diameter on the circumference)
x+y+a=180°(angles of a ∆ have sum =180°)
x+55°+90°=180°
x=35°.

Thankyou hope it helps❤️❤️