Question

if x and y are supplementary angles, then x and y are ____ vertical.
a. always
b. sometimes
c. never

Explanation:

Step1: Recall the definitions

Supplementary angles: Two angles whose sum is \(180^{\circ}\). Vertical angles: Two non - adjacent angles formed by two intersecting lines, which are equal.

Step2: Analyze the relationship

Let's assume \(x + y=180^{\circ}\) (supplementary). For vertical angles, they are formed by the intersection of two lines. If \(x\) and \(y\) are supplementary, they can only be vertical angles when \(x = y=90^{\circ}\) (in the case of two intersecting perpendicular lines). In most cases, if \(x + y = 180^{\circ}\), \(x
eq y\) (e.g., \(x = 30^{\circ}\), \(y = 150^{\circ}\)).

Answer:

B. Sometimes