Question

the measure of \\( \angle gux \\) can be calculated. \\( m \angle gux = 90 ^ { \circ } \\) reason:

Explanation:

Step1: Find the measure of the straight - angle

A straight - angle has a measure of \(180^{\circ}\). Given that one of the adjacent angles to \(\angle GUX\) (the angle formed by the intersection of the line and the ray) is \(40^{\circ}\), and we assume the other non - \(\angle GUX\) part of the straight - angle is also \(40^{\circ}\) (by the property of vertical angles or angle - construction symmetry in this diagram context).

Step2: Calculate \(\angle GUX\)

Using the formula for the measure of an angle in a straight - line \(m\angle GUX=180^{\circ}- 40^{\circ}-50^{\circ}\) (assuming the two non - \(\angle GUX\) angles are \(40^{\circ}\) each, which is a common geometric - figure property for such symmetric ray - line intersection diagrams).

Answer:

\(m\angle GUX = 90^{\circ}\) because the sum of angles on a straight line is \(180^{\circ}\), and if the two non - \(\angle GUX\) adjacent angles (by symmetry or vertical - angle - like property in the diagram) are \(40^{\circ}\) each, then \(180-(40 + 50)=90\) (assuming the non - \(\angle GUX\) angles sum to \(90^{\circ}\) based on the straight - line angle property).