Complete the following statements to prove that ∠ikl and ∠jld are supplementary angles. it is given that ∠eij ≅ ∠gji. also, ∠eij ≅ ∠ikl and ∠gji ≅ ∠jlk, as they are corresponding angles for parallel lines cut by a transversal. by the definition of congruent angles, m∠eij = m∠gji, m∠eij = m∠ikl, and m∠gji = m∠jlk. so, m∠ikl = m∠jlk by the . angle jlk and ∠jld are supplementary angles by the , so m∠jlk + m∠jld = 180°. by the , m∠ikl + m∠jld = 180°. therefore, ∠ikl and ∠jld are supplementary angles by definition.