Question

given: w ∥ x and y is a transversal. prove: ∠3 and ∠5 are supplementary. 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 corresponding angles theorem. 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 drop - down menu. by the drop - down menu, m∠3 + m ∠1 = drop - down menu. m∠1 to get m∠3 drop - down menu. re supplementary.

Explanation:

Step1: Recall Linear Pair Postulate

A linear pair of angles is formed when two adjacent angles form a straight line, and they are supplementary (sum to \(180^\circ\)). The linear pair postulate states that if two angles form a linear pair, then they are supplementary.

Step2: Identify the Correct Reason

\(\angle 3\) and \(\angle 1\) form a linear pair (they are adjacent and form a straight line on line \(y\)). So, by the linear pair postulate, they are supplementary. The other options: "definition of a linear pair" describes what a linear pair is, "definition of supplementary angles" is about angles summing to \(180^\circ\) (not the postulate for linear pairs), and "vertical angles theorem" is about vertical angles being congruent (not related here). So the correct choice is "linear pair postulate".

Answer:

linear pair postulate