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To solve the problem, we need to find the measures of angles \( x \) and \( y \) given that one of the angles in the diagram is 68°.

### Step 1: Identify Relationships Between Angles
- **Angle \( x \) and the 68° angle**: These two angles are vertically opposite angles, meaning they are equal.
  \[
  x = 68^\circ
  \]

- **Angle \( y \) and the 68° angle**: The angle labeled \( y \) is adjacent to the 68° angle and they form a linear pair. The angles in a linear pair add up to 180°.
  \[
  y + 68^\circ = 180^\circ
  \]
  Solving for \( y \):
  \[
  y = 180^\circ - 68^\circ = 112^\circ
  \]

### Step 2: Conclusion
- \( x = 68^\circ \)
- \( y = 112^\circ \)

Would you like further details or have any other questions?

### Related Questions:
1. What are vertically opposite angles and why are they equal?
2. How do you identify a linear pair of angles in a diagram?
3. Can two angles both be greater than 90° in a linear pair? Why or why not?
4. What are supplementary angles, and how do they differ from complementary angles?
5. If one angle is known, how can you find all other angles formed by intersecting lines?

### Tip:
Remember that vertically opposite angles are always equal, and linear pairs of angles always sum to 180°. This can help you quickly solve many angle-related problems!

Learn how to find the measures of angles x and y in a geometric diagram where one angle is known to be 68°. This problem involves using concepts such as vertically opposite angles and linear pairs of angles to determine the values of x and y. Suitable for Grades 7-9 students studying geometry.

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