The diagram shows two angles, $2x^\circ$ and $(5x - 22)^\circ$, and the problem states that these angles are complementary. Complementary angles sum up to 90 degrees.

Thus, the equation to solve is:

$2x + (5x - 22) = 90$

Now, simplifying this equation:

$2x + 5x - 22 = 90$

$7x - 22 = 90$

$7x = 112$

$x = \frac{112}{7} = 16$

The correct answer corresponds to option A, where the equation $2x + 5x - 22 = 90$ is presented.

Would you like further details or clarifications on this solution?

Here are 5 related questions to consider:

1. What are supplementary angles, and how do they differ from complementary angles?
2. If two angles add up to 180 degrees, what is their relationship called?
3. How would you solve an equation if you had three angles that are complementary?
4. What are some real-life examples of complementary angles?
5. Can complementary angles ever be obtuse?

Tip: When solving angle problems, always verify whether the angles are complementary or supplementary before setting up your equation!