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 ∠ikl, and m ∠gji = m ∠jlk. so, m ∠ikl = m ∠jlk by the (1.) angle jlk and ∠jld are supplementary angles by the (2.) so m ∠jlk + m ∠jld = 180 degrees. by the (3.) m ∠ikl + m ∠jld = 180 degrees. therefore, ∠ikl and ∠jld are supplementary angles by definition.

options for number one:

a. substitution property of equality

b. symmetric property of equality

c. subtraction property of equality

options for number two:

a. linear pair theorem

b. vertical angles theorem

c. congruent supplements theorem

options for number three:

a. substation property of equality

b. division property of equality

c. reflexive property of equality