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To solve for \(x\), we can use the fact that the angles along a straight line add up to \(180^\circ\). This means the sum of the two given angles must equal \(180^\circ\).

We have two angles:
- One is \(34^\circ\),
- The other is \((1 + 5x)^\circ\).

Thus, the equation becomes:
\[
34^\circ + (1 + 5x)^\circ = 180^\circ
\]

Let's solve for \(x\):

\[
34 + 1 + 5x = 180
\]
\[
35 + 5x = 180
\]
\[
5x = 180 - 35
\]
\[
5x = 145
\]
\[
x = \frac{145}{5}
\]
\[
x = 29
\]

Therefore, the value of \(x\) is \(29\).

Would you like more details or have any further questions?

Here are five related questions to expand on this:
1. How do you solve for unknown angles in a triangle?
2. What is the sum of the interior angles of a triangle?
3. How can you use the exterior angle theorem to solve for \(x\)?
4. How does the concept of supplementary angles apply to straight lines?
5. How would the solution change if the second angle was in terms of another variable?

**Tip:** Always remember that angles on a straight line are supplementary, meaning they sum up to \(180^\circ\).

Learn how to find the value of x by solving an equation using supplementary angles. This problem covers key mathematical concepts like linear equations and angle relationships, suitable for students in Grades 6-8. A step-by-step solution is provided, demonstrating the application of the supplementary angles theorem.

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