The image shows two angles with values: $112^\circ$ and $(3x + 11)^\circ$, along with red arrows indicating that these angles may be adjacent. Given the appearance, these angles likely form a linear pair, meaning they add up to $180^\circ$.

To solve for $x$:

1. Since the angles form a linear pair, their sum is $180^\circ$. So, $112^\circ + (3x + 11)^\circ = 180^\circ$

2. Simplify the equation: $112 + 3x + 11 = 180$ $123 + 3x = 180$

3. Subtract 123 from both sides: $3x = 180 - 123$ $3x = 57$

4. Divide both sides by 3: $x = \frac{57}{3}$ $x = 19$

Thus, the value of $x$ is 19.

Would you like further clarification or details on this solution?

Here are 5 related questions:

1. How do you solve for $x$ when angles form supplementary pairs?
2. Can adjacent angles be non-supplementary?
3. How do vertical angles relate to each other in a similar context?
4. What happens if the angles do not form a linear pair but instead a triangle?
5. Can angles greater than 180° exist in a real-world problem like this?

Tip: When working with angle pairs, remember that linear pairs always add up to 180°, while vertical angles are congruent.