Eij ? ? ikl and ? gji ? ? jlk, as they are corresponding angles for parallel lines cut by a transversal. therefore, if ? eij ? ? gji, then ? ikl ? ? jlk by the . then, ? jlk and ? jld are supplementary angles by the , so m? jlk + m? jld = 180°. since ? ikl ? ? jlk, m? ikl = m? jlk. thus m? ikl + m? jld = 180° by the .