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in the figure, ab || cd and ∠eij ≅ ∠gji.

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.