The problem shows two angles: one labeled as $2x^\circ$ and another labeled as $(4x + 108)^\circ$. These two angles appear to form a linear pair, meaning they are supplementary (their sum is $180^\circ$).

Let's set up the equation:

$2x + (4x + 108) = 180$ Now, let's solve for $x$.

1. Combine like terms: $6x + 108 = 180$

2. Subtract 108 from both sides: $6x = 72$

3. Divide by 6: $x = 12$

Thus, the value of $x$ is $12$.

Would you like more details or have any questions about this? Here are five related questions to explore further:

1. What is the total sum of angles in a linear pair?
2. How do you check if two angles are supplementary?
3. What if the angles formed a right angle instead of a straight line?
4. Can two angles be supplementary if both are acute?
5. How would the problem change if the second angle was $(5x + 108)^\circ$?

Tip: Always check for angle relationships like supplementary (sum = 180°) or complementary (sum = 90°) when solving problems involving unknown angles.