Given: r || s and q is a transversalProve: ∠4 is supplementary to ∠6Given that r || s and q is a transversal, we know that∠3 ≅ ∠6 by the .blank. 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.

Answer:Given: [tex]r || s[/tex] and q is a transversal. Alternative Interior Angle states that  a pair of angles on the inner side of each of those two lines but on opposite sides of the transversal are equal.By alternative interior angle; [tex]\angle 3 \cong \angle 6[/tex]Definition of Congruent angles are angles that have the same degree of measurement.Therefore, [tex]m\angle 3 = m\angle 6[/tex]    [By definition of Congruent]  .....[1]Linear Pair states that a pair of adjacent angles formed when two lines are intersect.therefore, [tex]\angle 4[/tex] and [tex]\angle 3[/tex] are a linear pair.   [by definition of linear pair]Two angles of linear pairs are always supplementary , which means their measure are add up to 180 degree.By the definition of supplementary angles, [tex]m\angle 4 + m\angle 3 = 180^{\circ}[/tex]                 .....[2]Substitute equation [1] in [2] we get,[tex]m\angle 4 +m\angle 6 =180^{\circ}[/tex]By the definition of supplementary angles, [tex]\angle 4[/tex] is supplementary to [tex] \angle 6[/tex]   Hence proved!