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In the given problem, we have two straight lines, \( AB \) and \( CD \), intersecting at point \( O \). The angles formed around point \( O \) include \( 170^\circ \) and two unknown angles represented as \( 5x \) and \( 4x \).

### Key Geometrical Concepts:
- The angles around a point sum up to \( 360^\circ \).
- The total angle formed by the straight line at point \( O \) (between lines \( AB \) and \( CD \)) is \( 180^\circ \).

### Equation Setup:
The total of the angles around point \( O \) should equal \( 360^\circ \). The angles provided are:
- \( 5x \) (angle \( AOK \))
- \( 4x \) (angle \( COL \))
- \( 170^\circ \) (the given external angle \( DOB \))

So, the equation for the sum of these angles is:

\[
5x + 4x + 170^\circ = 360^\circ
\]

### Solving for \( x \):

\[
9x + 170^\circ = 360^\circ
\]

Subtracting \( 170^\circ \) from both sides:

\[
9x = 360^\circ - 170^\circ = 190^\circ
\]

Now, divide by 9:

\[
x = \frac{190^\circ}{9} \approx 21.11^\circ
\]

### Final Answer:
\( x \approx 21.11^\circ \)

Let me know if you need more details or further clarification!

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**Relative Questions:**
1. What would happen if \( AB \) and \( CD \) were not straight lines?
2. How do we handle situations where the sum of angles around a point exceeds \( 360^\circ \)?
3. Can you explain how linear pairs of angles relate to this problem?
4. How would the equation change if the angle \( DOB \) was different?
5. What would happen if one of the angles was a right angle?

**Tip:** Always check the sum of angles around a point to ensure it equals \( 360^\circ \), as this helps verify the correctness of your calculations.

If AB and CD are straight lines, find x in the given diagram where angles 5x, 4x, and 170 degrees are shown.

Solve a geometry problem where AB and CD are straight lines and the angles 5x, 4x, and 170 degrees are provided. Learn the step-by-step process of finding x by using the sum of angles around a point theorem.

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