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In this problem, we have two angles: one given as \( 120^\circ \) and the other as \( (x - 30)^\circ \). The two angles appear to form a pair of supplementary angles, as they are on a straight line created by two intersecting lines. 

### Step 1: Identify the Angle Relationship
The angles are on a straight line, which makes them **supplementary angles**. Supplementary angles add up to \( 180^\circ \).

### Step 2: Set Up the Equation
Since supplementary angles add to \( 180^\circ \), we can write the equation:
\[
120^\circ + (x - 30)^\circ = 180^\circ
\]

### Step 3: Solve for \( x \)
Now, solve the equation step by step:
\[
120 + x - 30 = 180
\]
\[
x + 90 = 180
\]
\[
x = 180 - 90
\]
\[
x = 90
\]

So, the value of \( x \) is \( 90^\circ \).

### Final Answer:
- **Angle Relationship:** The angles are **supplementary**.
- **Value of \( x \):** \( x = 90^\circ \).

Do you want more details on this? Let me know if you have any questions!

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Here are five related questions for deeper exploration:
1. What is the difference between supplementary and complementary angles?
2. How do you solve for \( x \) when the angles are complementary instead?
3. Can two adjacent angles on the same line ever be less than \( 180^\circ \)?
4. What is the relationship between vertically opposite angles?
5. How would the equation change if the angles were not on a straight line?

### Tip:
For any pair of angles on a straight line, always check if they are supplementary by adding up to \( 180^\circ \).

Name the angle relationship and find x, where one angle is 120° and the other is (x - 30)°.

Learn how to solve for x in a geometry problem involving supplementary angles. The problem asks for the relationship between a 120° angle and (x - 30)°, which form a straight line. Suitable for students in Grades 6-8.

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