Question

find the longest side of \\( \triangle xyz \\), given that \\( m \angle z = 108 ^ { \circ } \\), \\( m \angle x = 30 ^ { \circ } \\), and \\( m \angle y = 42 ^ { \circ } \\).

Explanation:

Step1: Recall the triangle side - angle relationship

In a triangle, the larger the angle, the longer the side opposite it.

Step2: Compare the given angles

We have \(m\angle Z = 108^{\circ}\), \(m\angle Y=42^{\circ}\), \(m\angle X = 30^{\circ}\). Since \(108^{\circ}>42^{\circ}>30^{\circ}\).

Step3: Identify the side opposite the largest angle

The side opposite \(\angle Z\) is \(XY\).

Answer:

\(XY\)