In Fig. 16. 136, O is the centre of the circle, prove that x=y+z.

We have,

3 = 4 (Angle on same segment)


By degree measure theorem,


x = 2 3


x = 3 + 3


x = 3 + 4 (i) (Therefore, 3 = 4)


But,


y = 3 + 1 (By exterior angle property)


3 = y - 1 (ii)


From (i) and (ii),


x = y - 1 + 4


x = y + 4 - 1


x = y + z + 1 - 1 (By exterior angle property)


x = y + z


Hence, proved


7