In the Fig, O is the centre of the circle, prove that,  ∠a = ∠b + ∠c.
 

∠AOB = 2∠AEB = 2∠AFB 
.^.. ∠AOB = ∠AEB + ∠AFB 
.^.. ∠a = ∠4 + ∠3 = 2∠4   ............. (i)
Now ∠1 = ∠2     (In same segment)    ............. (ii)
∠b = ∠4 + ∠1         (Exterior angles equal to sum of two equal interior opposite angles)
⇒ ∠b = ∠4+∠2         ............. (iii)  [from (ii)]
∠c = ∠4 - ∠2              ............. (iv) (Since  ∠c +∠2 = ∠4)
Adding equations (iii) and (iv) we get,
∠b + ∠c = 2∠4 = ∠a     [from(i)]
or ∠a = ∠b + ∠c