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Solve for x
in the following diagram, given that the bottom line segment is a straight line:

To solve for \(x\) in this diagram, we can use the fact that the sum of the angles around a point on a straight line is \(180^\circ\).

### Step-by-step approach:

1. **Identify the angles:**
   The diagram shows the following angles around the point where the rays intersect the straight line:
   - \(2x^\circ\) (far left)
   - \(x^\circ\) (next to it)
   - \((x + 30)^\circ\) (middle)
   - \((x + 40)^\circ\) (far right)

2. **Set up the equation:**
   Since these angles are on a straight line, their sum must equal \(180^\circ\).

   \[
   2x + x + (x + 30) + (x + 40) = 180
   \]

3. **Simplify the equation:**
   Combine like terms:
   \[
   2x + x + x + x + 30 + 40 = 180
   \]
   \[
   5x + 70 = 180
   \]

4. **Solve for \(x\):**
   Subtract 70 from both sides:
   \[
   5x = 110
   \]
   Divide by 5:
   \[
   x = 22
   \]

Thus, the value of \(x\) is **22 degrees**.

Would you like further details or have any questions?

### Related Questions:
1. How do we know that the angles sum to \(180^\circ\) in this scenario?
2. What would change if the line were not straight but curved?
3. Can you explain how combining like terms works in this context?
4. How would we proceed if the diagram provided angles in radians instead of degrees?
5. How does this solution apply to general problems involving supplementary angles?

### Tip:
When dealing with angles on a straight line, always check that the sum equals \(180^\circ\), as this is a common and crucial property.

Solve for x in the following diagram, given that the bottom line segment is a straight line.

Learn how to solve for x in a geometry problem involving the sum of angles on a straight line. This step-by-step solution explains key concepts like angle properties, supplementary angles, and algebraic simplification. Suitable for students in Grades 6-8.

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