Question

find the measure of ∠x in the figure.

Explanation:

Step1: Identify angle sum

The total angle around a point (or the sum of angles in a right - related figure here) should be considered. We know that the sum of the angles \(38^{\circ}\), \(90^{\circ}\) and \(x\) should be \(180^{\circ}\) (since they form a linear pair or a straight - line - related angle sum, assuming the figure is such that these angles add up to a straight angle). So the equation is \(38^{\circ}+90^{\circ}+x = 180^{\circ}\)? Wait, no, looking at the figure, actually, the three angles (the right angle \(90^{\circ}\), the \(38^{\circ}\) angle, and \(x\)) seem to be related such that \(x=90^{\circ} + 38^{\circ}\)? Wait, no, let's re - examine. The figure has a right angle (\(90^{\circ}\)), a \(38^{\circ}\) angle, and angle \(x\). Wait, maybe it's a case where \(x\) is the sum of the right angle and the \(38^{\circ}\) angle? Wait, no, let's think again. If we have two rays, one forming a right angle with the vertical, and another at \(38^{\circ}\) from the horizontal, then the angle \(x\) between the horizontal and the vertical (the right angle) plus the \(38^{\circ}\) angle? Wait, no, the correct approach: the angle \(x\) is composed of the right angle (\(90^{\circ}\)) and the \(38^{\circ}\) angle? Wait, no, looking at the diagram, the three angles (the \(38^{\circ}\), the \(90^{\circ}\), and \(x\)) – wait, no, actually, the angle \(x\) is equal to \(90^{\circ}+38^{\circ}\). Let's calculate that.

Step2: Calculate \(x\)

\(x = 90^{\circ}+38^{\circ}\)
\(x=128^{\circ}\)

Wait, maybe I made a mistake. Wait, another approach: if we consider that the sum of angles on a straight line is \(180^{\circ}\), and we have a right angle (\(90^{\circ}\)) and a \(38^{\circ}\) angle, then \(x = 180^{\circ}-(90^{\circ} - 38^{\circ})\)? No, that doesn't make sense. Wait, let's look at the diagram again. The diagram has a right angle (the small square indicates \(90^{\circ}\)), a \(38^{\circ}\) angle, and angle \(x\). So the angle \(x\) is the sum of the right angle and the \(38^{\circ}\) angle. So \(x=90 + 38=128\) degrees.

Answer:

\(128^{\circ}\)