https://file.aiquickdraw.com/mathbot/file/1729968235358a9l4w849.jpg

To find the value of \( x \) and \( 3x \) in this problem, let's analyze the shape and angles provided.

### Step-by-Step Solution

1. **Identify the Relevant Angles:**
   The diagram shows a shape with angles labeled as \( 45^\circ \), \( 135^\circ \), \( 3x^\circ \), \( x^\circ \), \( 45^\circ \), and \( 135^\circ \).

2. **Determine the Total Interior Angle Sum:**
   The shape has a "zigzag" line, so we can use angle relationships around a straight line. In this case, the interior angles on a straight line add up to \( 180^\circ \) for each "corner."

3. **Set Up the Equation for \( 3x \):**
   The two adjacent angles \( 3x^\circ \) and \( x^\circ \) are part of a straight line, where their sum equals \( 180^\circ \). Therefore, we have:
   \[
   3x + x = 180
   \]
   \[
   4x = 180
   \]

4. **Solve for \( x \):**
   Divide both sides by 4:
   \[
   x = \frac{180}{4} = 45
   \]

5. **Calculate \( 3x \):**
   Now that we know \( x = 45 \), we can find \( 3x \) by substituting \( x \):
   \[
   3x = 3 \times 45 = 135
   \]

### Answers

- \( x = 45^\circ \)
- \( 3x = 135^\circ \)

Would you like more details or have any questions about this solution?

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Here are some related questions to explore further:

1. How would the solution change if the angles on the shape were altered?
2. Can you identify other angle pairs that add up to \(180^\circ\) in different shapes?
3. What if \(x\) was given, how could we solve for other angles around it?
4. How does knowing properties of straight lines and angles help in geometry problems?
5. Can you think of other shapes where we could use similar strategies to find unknown angles?

**Tip:** Always remember that angles on a straight line add up to \(180^\circ\), which is a useful property for solving many geometry problems.

Learn how to solve for x and 3x in a geometry problem involving angles on a straight line. This step-by-step solution uses fundamental angle properties and the Straight Angle Theorem, making it ideal for students in Grades 6-8.

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