Given: Δ ABC, BC = AB and ∠B = 80°

As BC = AB

So it is an isosceles triangle.

let ∠C = ∠A = x

∠B = 80° (given)

As we know, ∠A + ∠B + ∠C = 180°

⇒ x + 80° + x = 180°

⇒ 2x = 180° - 80°

⇒ 2x = 100°

⇒ x = 50°

So, ∠C = ∠A = 50°

Hence, option C is correct.