In given that,

x = ∠A + ∠B (Exterior angles)

z = ∠A (Vertically opposite angles)

y = ∠A + ∠C (Exterior angles)

We know that,

∠A + ∠B + ∠C= 180^o

z + x - ∠A + y - ∠A = 180^o

-z = 180^o – x – y

z = x + y – 180^o