https://file.aiquickdraw.com/mathbot/file/1727246189548kh87yh66.jpg

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).

Question 16: Solve for x. The image shows three angles with algebraic expressions labeled as 10° - 2x, 3x, and 20° - 2.5x.

Learn how to solve for x in a problem involving angles and algebraic expressions. This example demonstrates the use of the Straight Angle Theorem and algebraic manipulation, suitable for students in Grades 8-10.

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