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The given problem states that the angles are supplementary, which means their sum is \(180^\circ\).

The two angles provided are:
- \(114^\circ\)
- \((3x + 9)^\circ\)

Since the angles are supplementary, their sum must equal \(180^\circ\):
\[
114^\circ + (3x + 9)^\circ = 180^\circ
\]

Now, let's solve for \(x\):

1. Combine like terms:
\[
114 + 3x + 9 = 180
\]
\[
123 + 3x = 180
\]

2. Subtract 123 from both sides:
\[
3x = 180 - 123
\]
\[
3x = 57
\]

3. Divide by 3:
\[
x = \frac{57}{3}
\]
\[
x = 19
\]

So, \(x = 19\).

Would you like more details or have any questions about this solution?

Here are 5 related questions you might find interesting:
1. What is the definition of supplementary angles?
2. How do you solve for unknowns in angles when they are complementary?
3. What would change if the angles were labeled as complementary instead of supplementary?
4. How can you verify your answer using substitution?
5. How would the problem differ if the angles were expressed in terms of \(x^2\) instead of linear expressions?

**Tip:** Always verify your final answer by substituting the value of \(x\) back into the angle expressions to ensure the total equals \(180^\circ\).

Solve for X in the given problem with supplementary angles (114° and (3x + 9)°).

Learn how to solve for X in a problem involving supplementary angles. The two angles provided are 114° and (3x + 9)°, which sum to 180°. This step-by-step solution explains how to solve for X using algebra and the supplementary angles theorem. Suitable for students in Grades 7-9.

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