Question

1. solve for x. (resolver x)

Explanation:

Step1: Identify angle sum

The angles \(2x^\circ\), \(32^\circ\), and \(90^\circ\) form a right angle (sum to \(90^\circ\)). So, \(2x + 32 + 90 = 180\)? Wait, no—wait, the horizontal and vertical lines are perpendicular, so the angle between the horizontal (left - right) and vertical (up - down) is \(90^\circ\). The three angles \(2x^\circ\), \(32^\circ\), and the right angle? Wait, no, looking at the diagram: the horizontal line, the vertical line (with right angle), and the two other lines. So the angle between the horizontal (left part) and the slanted line is \(2x^\circ\), between the slanted line and vertical is \(32^\circ\), and vertical and horizontal (right) is \(90^\circ\). So the sum of \(2x^\circ\), \(32^\circ\), and \(90^\circ\)? No, wait, actually, the three angles on the left - hand side of the vertical line: \(2x^\circ\), \(32^\circ\), and the right angle? Wait, no, the horizontal line is straight, so the angle between the negative x - axis, the slanted line, and the positive y - axis: the sum of \(2x\), \(32^\circ\), and \(90^\circ\) should be \(180^\circ\)? No, wait, the vertical line is perpendicular to the horizontal, so the angle between the horizontal (left) and vertical (up) is \(90^\circ\), which is split into \(2x\) and \(32^\circ\). Wait, that makes more sense: \(2x + 32 = 90\), because they are complementary (add up to \(90^\circ\)) since the vertical and horizontal are perpendicular.

Step2: Solve for x

Start with the equation \(2x + 32 = 90\).
Subtract 32 from both sides: \(2x = 90 - 32\)
\(2x = 58\)
Divide both sides by 2: \(x=\frac{58}{2}=29\)

Answer:

\(x = 29\)