https://file.aiquickdraw.com/mathbot/file/1725934433183ra9tvl3m.jpg

In this diagram, the two angles are adjacent and form a straight line. Since the sum of angles on a straight line is always \(180^\circ\), we can set up the following equation based on the provided angles:

\[
57^\circ + (3x - 3)^\circ = 180^\circ
\]

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

\[
57 + (3x - 3) = 180
\]

Simplifying the left-hand side:

\[
57 - 3 + 3x = 180
\]
\[
54 + 3x = 180
\]

Next, subtract 54 from both sides:

\[
3x = 180 - 54
\]
\[
3x = 126
\]

Now, divide both sides by 3:

\[
x = \frac{126}{3} = 42
\]

Thus, the value of \(x\) is \(42^\circ\).

Would you like more details or have any questions?

### Related Questions:
1. What are adjacent angles, and how do they relate to this problem?
2. Can you explain why the sum of angles on a straight line is \(180^\circ\)?
3. What is the difference between supplementary and complementary angles?
4. How would you set up an equation if the sum of the angles was not \(180^\circ\) but \(90^\circ\)?
5. What if the angle expression was in terms of \(x^2\), how would that change the solution?

### Tip:
Always remember that adjacent angles on a straight line are supplementary, meaning they add up to \(180^\circ\).

What is the value of x? (involves adjacent angles on a straight line, with one angle given as 57° and the other as (3x - 3)°)

In this problem, you will learn how to find the value of x by using the concept of adjacent angles forming a straight line. The sum of angles is 180°, and we solve for x using basic algebra. Suitable for students in Grades 7-9.

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