Given: r || s and q is a transversal prove: ∠4 is supplementary to ∠6 given that r || s and q is a transversal, we know that ∠3 ≅ ∠6 by the . therefore, m∠3 = m∠6 by the definition of congruent. we also know that, by definition, ∠4 and ∠3 are a linear pair, so they are supplementary by the linear pair postulate. by the definition of supplementary angles, m∠4 + m∠3 = 180°. using substitution, we can replace m∠3 with m∠6 to get m∠4 + m∠6 = 180°. therefore, by the definition of supplementary angles, ∠4 is supplementary to ∠6.