Question

classify the angle pair \\( \angle v u x \\) and \\( \angle x u t \\).
adjacent and neither complementary nor supplementary
a linear pair
nonadjacent and supplementary
adjacent and complementary

Explanation:

Step1: Recall the definition of adjacent angles

Adjacent angles have a common vertex and a common side. $\angle VUX$ and $\angle XUT$ have a common vertex \(U\) and a common side \(UX\).

Step2: Recall the definition of supplementary angles

Supplementary angles sum to \(180^{\circ}\). Calculate the sum of \(\angle VUX\) and \(\angle XUT\). Since \(\angle VUX+\angle XUT = 180^{\circ}\) (because they form a straight - line along \(TV\)).

Step3: Recall the definition of non - adjacent angles

Non - adjacent angles do not share a common side. But \(\angle VUX\) and \(\angle XUT\) share a common side \(UX\), so they are not non - adjacent.

Step4: Recall the definition of a linear pair

A linear pair is a pair of adjacent angles whose non - common sides are opposite rays. Here, the non - common sides \(UV\) and \(UT\) are opposite rays (since \(TV\) is a straight line).

Answer:

A linear pair