https://file.aiquickdraw.com/mathbot/file/172686279409301o8mext.jpg

Examine the diagram above and determine the following:

The angle relationship is

The value of x is equal to

The measure of the angle in bold is

The diagram shows two parallel lines cut by a transversal, forming two angles. The given angles, labeled as \(33x - 2\) and \(31x + 6\), are corresponding angles since they are in matching positions relative to the parallel lines and the transversal.

### 1. **Angle Relationship**: 
Since the angles are corresponding angles formed by a transversal cutting through parallel lines, they must be **equal**. This gives the equation:
\[
33x - 2 = 31x + 6
\]

### 2. **Solve for \(x\)**:
To find the value of \(x\), solve the equation:

\[
33x - 2 = 31x + 6
\]

First, subtract \(31x\) from both sides:

\[
33x - 31x - 2 = 6
\]
\[
2x - 2 = 6
\]

Now, add 2 to both sides:

\[
2x = 8
\]

Finally, divide by 2:

\[
x = 4
\]

### 3. **Measure of the Bold Angle**:
To find the measure of the bold angle labeled as \(33x - 2\), substitute \(x = 4\) into the expression:

\[
33(4) - 2 = 132 - 2 = 130^\circ
\]

### Summary:
- **Angle Relationship**: The angles are corresponding and thus equal.
- **Value of \(x\)**: \(x = 4\)
- **Measure of the Bold Angle**: \(130^\circ\)

Would you like more details or have any questions?

Here are 5 related questions:
1. What are alternate interior angles, and how do they relate to parallel lines?
2. How would you solve if the angles were supplementary instead of equal?
3. How can you verify that two lines are parallel using angle relationships?
4. What happens to the value of \(x\) if the angles were supplementary?
5. What is the relationship between exterior and interior angles in parallel lines?

**Tip**: When working with parallel lines and a transversal, always look for angle relationships like corresponding, alternate interior, or alternate exterior angles to solve problems efficiently.

Examine the diagram above and determine the following:
The angle relationship is
The value of x is equal to
The measure of the angle in bold is

Discover how to solve for angles and variables using the corresponding angles postulate with parallel lines cut by a transversal. This tutorial provides a step-by-step guide to finding the value of x and the angle measure using algebra and geometry principles. Suitable for students in Grades 7-10.

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