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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.

Find the value of x. The problem shows two angles: one labeled as (2x)° and another labeled as (4x + 108)°. These two angles appear to form a linear pair, meaning they are supplementary (their sum is 180°).

Learn how to solve for x in a problem involving a linear pair of angles, where one angle is labeled as (2x)° and the other as (4x + 108)°. This step-by-step solution explains how to use algebra and the linear pair theorem to find the value of x. Suitable for students in Grades 8-10.

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