https://file.aiquickdraw.com/mathbot/file/17249011305315e1lso4z.jpg

The image shows a pair of adjacent angles formed by two intersecting lines. The problem is to find the value of \( x \) given the expressions for the two angles. Let's solve it step by step.

### Step 1: Identify the relationship between the angles
The two angles are adjacent and form a straight line. This means that they are supplementary, so their sum is \( 180^\circ \).

### Step 2: Set up the equation
The expressions given for the angles are:
- One angle: \( 6x + 12 \)
- Other angle: \( 3x - 3 \)

Since the angles are supplementary:
\[
(6x + 12) + (3x - 3) = 180
\]

### Step 3: Simplify the equation
Combine like terms:
\[
6x + 3x + 12 - 3 = 180
\]
\[
9x + 9 = 180
\]

### Step 4: Solve for \( x \)
Subtract 9 from both sides:
\[
9x = 171
\]
Divide by 9:
\[
x = 19
\]

### Conclusion
The value of \( x \) is \( \boxed{19} \).

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

Here are some related questions to deepen your understanding:
1. What is the measure of each angle when \( x = 19 \)?
2. How do you identify whether angles are supplementary or complementary?
3. What is the difference between adjacent and vertical angles?
4. Can two angles be adjacent and non-supplementary? Provide an example.
5. What are the properties of supplementary angles on a straight line?

**Tip:** When dealing with angles, always check the type of angle relationship (complementary, supplementary, etc.) to set up the correct equation.

Learn how to find the value of x in a problem involving supplementary angles formed by intersecting lines. Step-by-step solution provided with expressions and equations. Suitable for high school students.

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