https://file.aiquickdraw.com/mathbot/file/17281697139514jcivbt5.jpg

Let's determine the values of \( x \), \( y \), and \( z \) using geometric principles.

1. **Angle \( y \)**: This angle is given as 68° directly in the image.
   \[
   y = 68^\circ
   \]

2. **Angle \( z \)**: The sum of angles in a triangle is always 180°. Using this, we can calculate angle \( z \).
   \[
   z = 180^\circ - 72^\circ - 68^\circ = 40^\circ
   \]
   So, \( z = 40^\circ \).

3. **Angle \( x \)**: This angle is on a straight line, and a straight line always sums up to 180°. Since one of the angles adjacent to it is 72°, we can calculate \( x \) as:
   \[
   x = 180^\circ - 72^\circ = 108^\circ
   \]
   So, \( x = 108^\circ \).

### Final values:
- \( x = 108^\circ \)
- \( y = 68^\circ \)
- \( z = 40^\circ \)

Would you like more details on how these calculations were done?

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Here are five related questions to think about:
1. What is the sum of all interior angles of a polygon with more than three sides?
2. How do supplementary angles relate to each other?
3. Can a triangle have more than one obtuse angle? Why or why not?
4. What are complementary angles, and how are they different from supplementary angles?
5. How can you identify congruent triangles in geometric problems?

**Tip**: Always remember that the sum of angles in a triangle is 180°, and the sum of angles on a straight line is also 180°.

Learn how to determine the values of angles x, y, and z using geometric properties such as the triangle angle sum and supplementary angles on a straight line. Suitable for Grade 8-10 students.

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