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 $180^\circ$.