The image shows two adjacent angles with the following measures:

• One angle is $26^\circ$.
• The other angle is labeled as $(5x + 11)^\circ$.

These two angles form a linear pair because they share a common vertex and lie on a straight line. The sum of the angles in a linear pair is always $180^\circ$.

So, we can set up the equation as:

$26^\circ + (5x + 11)^\circ = 180^\circ$

Now, let's solve this:

$26 + 5x + 11 = 180$ $37 + 5x = 180$ $5x = 180 - 37$ $5x = 143$ $x = \frac{143}{5}$ $x = 28.6$

Therefore, the value of $x$ is $28.6$.

Let me know if you want more details or have any questions!

Here are five related questions to explore further:

1. What is the definition of supplementary angles?
2. How do you find the measure of each angle when two angles form a linear pair?
3. What would happen if the two angles did not form a straight line?
4. How can you use algebra to solve angle problems like this one?
5. What is the geometric property that guarantees the sum of the angles will be 180 degrees?

Tip: Always verify if angles form a straight line when calculating their sum in linear pairs.