https://file.aiquickdraw.com/mathbot/file/1728591605655an5ltdkx.jpg

The image shows two intersecting lines with given angles, and the task is to find the value of \( x \). Specifically, angle \( \angle PON \) is given as 158°, and angle \( \angle ONL \) is 68°.

### Step-by-step solution:

1. **Identify the relationship**:
   - The two given angles, \( \angle PON = 158^\circ \) and \( \angle ONL = 68^\circ \), are *supplementary*. This is because they are opposite angles formed by intersecting lines, and they sum up to 180°.

2. **Calculate the unknown angle**:
   - Since \( \angle PON + \angle ONL = 180^\circ \), we can set up the equation:
   \[
   x + 68^\circ = 180^\circ
   \]
   
3. **Solve for \( x \)**:
   \[
   x = 180^\circ - 68^\circ = 112^\circ
   \]

Thus, the value of \( x \) is **112°**.

Would you like any more details or have further questions?

Here are 5 related questions to explore:
1. What are vertically opposite angles, and how are they calculated?
2. How do we identify supplementary and complementary angles?
3. Can two angles be supplementary if they are not adjacent?
4. What is the sum of all angles around a point where two lines intersect?
5. How would the calculation change if one of the angles was missing?

**Tip**: Always check if angles are vertically opposite or supplementary when lines intersect!

What is the value of x given that angle PON = 158° and angle ONL = 68°?

Learn how to find the value of x when given that angles PON and ONL form supplementary angles in intersecting lines. This step-by-step solution is perfect for Grade 7 students exploring geometry and angles.

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