Question

use the figure shown. select all the true statements. a. x = y b. x + y = 180 c. y = z d. x + z = 180 e y + z = 180

Explanation:

Step1: Recall angle - pair relationships

Angles \(x\) and \(y\) are a linear - pair of angles. Linear - pair of angles are adjacent angles formed by two intersecting lines and their sum is \(180^{\circ}\), so \(x + y=180\).

Step2: Recall vertical - angle relationships

Angles \(y\) and \(z\) are vertical angles. Vertical angles are equal, so \(y = z\).

Step3: Recall linear - pair relationships for \(x\) and \(z\)

\(x\) and \(z\) are not a linear - pair.

Step4: Recall linear - pair relationships for \(y\) and \(z\)

\(y\) and \(z\) are not a linear - pair.

Answer:

B. \(x + y = 180\)
C. \(y = z\)