https://file.aiquickdraw.com/mathbot/file/1725922286850iph8yne1.jpg

In the image, we have two angles represented by the expressions \( 3x + 20 \) and \( 2x - 10 \), which appear to form a linear pair (angles that are adjacent and sum up to 180°). This means that:

\[
(3x + 20) + (2x - 10) = 180
\]

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

1. Combine like terms:
\[
3x + 20 + 2x - 10 = 180
\]
\[
5x + 10 = 180
\]

2. Subtract 10 from both sides:
\[
5x = 170
\]

3. Divide both sides by 5:
\[
x = 34
\]

Thus, \( x = 34 \).

### Verifying the Angles:
Now substitute \( x = 34 \) back into the expressions for the angles:

- \( 3x + 20 = 3(34) + 20 = 102 + 20 = 122^\circ \)
- \( 2x - 10 = 2(34) - 10 = 68 - 10 = 58^\circ \)

The sum is:
\[
122^\circ + 58^\circ = 180^\circ
\]

Thus, the solution is correct.

Would you like further details or clarifications?

### Relative Questions:
1. How do you identify a linear pair of angles?
2. Can angles on a straight line ever sum to more or less than 180°?
3. What happens if \( x \) results in a negative angle?
4. What other relationships between angles can help solve such problems?
5. How can you verify if angles are supplementary or complementary?

### Tip:
Always remember that angles forming a straight line (linear pair) will sum to 180°, which is a useful property in many geometric problems.

How to solve the problem where two angles formed by expressions 3x + 20 and 2x - 10 sum up to 180°?

Learn how to solve a linear pair problem where the angles formed by the expressions 3x + 20 and 2x - 10 sum up to 180°. This problem covers key concepts in algebra and geometry, including the Linear Pair Theorem. Suitable for students in Grades 6-8.

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