The image shows three angles with algebraic expressions. These angles are labeled as follows:

• $10^\circ - 2x$
• $3x$
• $20^\circ - 2.5x$

Since these angles form a straight angle (which sums to $180^\circ$), we can set up the following equation:

$(10^\circ - 2x) + 3x + (20^\circ - 2.5x) = 180^\circ$

Now, let's solve for $x$:

1. Combine like terms:

$10^\circ + 20^\circ + (-2x + 3x - 2.5x) = 180^\circ$

This simplifies to:

$30^\circ + (-1.5x) = 180^\circ$

2. Subtract 30° from both sides:

$-1.5x = 150^\circ$

3. Divide by -1.5 to isolate $x$:

$x = \frac{150^\circ}{-1.5} = -100^\circ$

Thus, $x = -100$.

Would you like further details on any step?

Here are 5 related questions to deepen your understanding:

1. What are supplementary angles, and why do these angles add up to 180°?
2. How do we handle negative angles in geometry?
3. How would the equation change if the angles formed a right angle instead of a straight angle?
4. Can you verify the solution by plugging $x = -100$ back into the original angle expressions?
5. How does the process of combining like terms work in algebra?

Tip: When solving for $x$, always check if the angles sum up to the correct total (e.g., 180° for a straight angle).