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The problem asks to find the value of \( x \), given the following conditions:

- \( m\angle 1 = (3x + 7)^\circ \)
- \( m\angle 2 = (2x - 2)^\circ \)

In the diagram, \( \angle 1 \) and \( \angle 2 \) seem to be supplementary angles because they are adjacent and form a straight line. Therefore, their sum must be \( 180^\circ \). 

We can set up the following equation:

\[
(3x + 7) + (2x - 2) = 180
\]

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

\[
3x + 7 + 2x - 2 = 180
\]

Simplifying:

\[
5x + 5 = 180
\]

Subtract 5 from both sides:

\[
5x = 175
\]

Divide both sides by 5:

\[
x = 35
\]

Thus, \( x = 35 \).

Let me know if you'd like more details or have any questions!

Here are 5 related questions:
1. What are supplementary angles?
2. How do you know when two angles are supplementary?
3. Can two acute angles ever be supplementary?
4. How do adjacent angles behave when they form a straight line?
5. How would the calculation change if \( m\angle 1 \) and \( m\angle 2 \) were complementary instead of supplementary?

**Tip:** When solving for \( x \), always double-check your equation to make sure you accounted for all terms correctly!

If m∠1 = (3x + 7)° and m∠2 = (2x - 2)°, what is the value of x?

Learn how to solve a linear equation involving supplementary angles where m∠1 = (3x + 7)° and m∠2 = (2x - 2)°. Detailed step-by-step solution included. Suitable for Grade 7-9 students learning about algebra and angle relationships.

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