Mathematics

Gwendolyn Mcintyre

15 August, 05:57

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.