Use the drop-down menus to complete the proof. Given that w ∥ x and y is a transversal, we know that ∠1 ≅∠5 by the . Therefore, m∠1 = m ∠5 by the definition of congruent. We also know that, by definition, ∠3 and ∠1 are a linear pair so they are supplementary by the . By the , m∠3 + m ∠1 = 180. Now we can substitute m∠5 for m∠1 to get m∠3 + m∠5 = 180. Therefore, by the definition of supplementary angles, ∠3 and ∠5 are supplementary.

Answer:From the graph attached, we know that [tex]\angle 1 \cong \angle 5[/tex] by the corresponding angle theorem, this theorem is about all angles that derive form the intersection of one transversal line with a pair of parallels. Specifically, corresponding angles are those which are placed at the same side of the transversal, one interior to parallels, one exterior to parallels, like [tex]\angle 1[/tex] and [tex]\angle 5[/tex].We also know that, by definition of linear pair postulate, [tex]\angle 3[/tex] and [tex]\angle 1[/tex] are linear pair. Linear pair postulate is a math concept that defines two angles that are adjacent and for a straight angle, which is equal to 180°.They are supplementary by the definition of supplementary angles. This definition states that angles which sum 180° are supplementary, and we found that [tex]\angle 3[/tex] and [tex]\angle 1[/tex] together are 180°, because they are on a straight angle. That is, [tex]m \angle 3 + m \angle 1 = 180\°[/tex]If we substitute [tex]\angle 5[/tex] for [tex]\angle 1[/tex], we have [tex]m \angle 3 + m \angle 5 = 180\°[/tex], which means that [tex]\angle 3[/tex] and [tex]\angle 5[/tex] are also supplementary by definition.