Question

how do i write a paragraph proof of this and what is the answer

Answer 1

From C you draw a parallel to AB. From left to right name the angles:
C₁, C₃ and C₂

∠C₁ = ∠A₁ (interior alternate)
∠C₃ = ∠C₃
∠C₂ = ∠B₂ (interior alternate), but ∠C₁ + ∠C₃ + ∠C₂ = 180° (straight line),

Then: ∠A₁ + ∠C₃ + ∠B₂ = 180°