https://file.aiquickdraw.com/mathbot/file/1726444579027v5kni7qv.jpg

To solve for \(x\) in the given diagram, let's analyze the geometry.

### Step-by-step breakdown:

1. **Identifying angles:**
   - Angle \(AOB = 90^\circ\) (it's a right angle, as indicated by the small square at point \(O\)).
   - Angle \(DOB = 170^\circ\) (given).
   - Angle \(AOD = 5x\) (labeled).
   - Angle \(BOC = 4x\) (labeled).

2. **Using the straight line property:**
   Since \(AB\) and \(CD\) are straight lines, angles on a straight line sum up to \(180^\circ\).
   
   At point \(O\), consider:
   - The sum of angles \(AOB + BOC + DOB = 180^\circ\) since they are angles on a straight line.
   
   Using this:
   \[
   90^\circ + 4x + 170^\circ = 180^\circ
   \]
   Simplifying:
   \[
   4x + 260^\circ = 180^\circ
   \]
   Subtract \(260^\circ\) from both sides:
   \[
   4x = -80^\circ
   \]
   Divide by 4:
   \[
   x = -20^\circ
   \]
   
Thus, the value of \(x = -20^\circ\).

This seems unusual, and indicates that further checks on how angles are marked could be needed. Let me know if you'd like further details, questions, or clarification! 

### Related Questions:
1. How can we identify supplementary angles in such problems?
2. What is the role of straight angles in this diagram?
3. How does the linear pair of angles help in solving this?
4. Can the angles in any polygon be calculated similarly?
5. What is the significance of a right angle in geometry?

**Tip:** When solving for angles, always verify the sum of angles at a point on a straight line adds to \(180^\circ\).

If shown, AB and CD are straight lines. Find x in the diagram.

Solve for x in a geometric diagram involving straight lines AB and CD. This problem includes the use of angles, straight line properties, and supplementary angles. Suitable for students in Grades 8-10.

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