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IF SHOWN AB AND CD ARE STRAIGHT LINES FIND X IN EACH CASE

To find \( x \), let's break down the information given in the problem:

1. The lines \( AB \) and \( CD \) are straight, and we are provided with angles around point \( O \). 
2. \( \angle AOK = 5x \), \( \angle BOC = 4x \), and the angle between these two is given as \( 170^\circ \).
3. Since \( \angle KOL \) is marked as a right angle, it measures \( 90^\circ \).

### Step-by-Step Solution
1. Since the point \( O \) forms angles around a straight line, the sum of all angles around \( O \) must be \( 360^\circ \).

   The total angles given:
   \[ \angle AOK + \angle KOL + \angle BOC + 170^\circ = 360^\circ \]

   Substituting the given expressions:
   \[ 5x + 90^\circ + 4x + 170^\circ = 360^\circ \]

2. Combine like terms:
   \[ 9x + 260^\circ = 360^\circ \]

3. Subtract \( 260^\circ \) from both sides to isolate \( 9x \):
   \[ 9x = 100^\circ \]

4. Divide by 9 to solve for \( x \):
   \[ x = \frac{100^\circ}{9} \approx 11.11^\circ \]

Thus, the value of \( x \) is approximately \( 11.11^\circ \).

Would you like a more detailed explanation or have any questions about this problem?

### Related Questions
1. What are the properties of supplementary angles and how are they used in geometry problems?
2. How do you find the angles around a point in more complex geometric shapes?
3. What is the sum of the interior angles in different types of polygons?
4. How would the problem change if one of the lines was not straight?
5. Can we use trigonometry to solve similar types of problems?

### Tip
Always check the sum of angles around a point; it should equal \( 360^\circ \). This is a useful property in many geometric problems.

If shown, AB and CD are straight lines. Find x in each case.

Solve for x using the angle properties of straight lines and points. This geometry problem involves calculating angles around a point, with straight lines AB and CD. Suitable for students in Grades 7-10.

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