https://file.aiquickdraw.com/mathbot/file/1726141718637i4023a70.jpg

Let's begin by addressing the first problem in the image:

**Problem 11:**  
*Find the values of x, y & z in the following parallelogram.*

From the properties of parallelograms, we know:
1. Opposite angles in a parallelogram are equal.
2. Adjacent angles in a parallelogram are supplementary (add up to 180°).

Looking at the diagram:
- The angle labeled \( z \) (at point C) is opposite to the angle labeled 50° (at point A). Therefore, \( z = 50^\circ \).
- The angle labeled \( y \) (at point D) is adjacent to the angle 70° (at point B). So, they must add up to 180°. Therefore:
  \[
  y + 70^\circ = 180^\circ \implies y = 110^\circ.
  \]
- Finally, the angle \( x \) (at point B) is adjacent to the angle labeled 50° (at point A). These must also add up to 180°, so:
  \[
  x + 50^\circ = 180^\circ \implies x = 130^\circ.
  \]

Thus, the values are:
- \( z = 50^\circ \)
- \( y = 110^\circ \)
- \( x = 130^\circ \)

Let me know if you'd like a breakdown for any of the other questions!

### Relative Questions:
1. What are the properties of angles in a parallelogram?
2. How can we find unknown angles when given supplementary pairs?
3. What is the difference between opposite and adjacent angles in a quadrilateral?
4. How would the angle values change if this was a rectangle instead of a parallelogram?
5. Can the internal angles of any quadrilateral always sum up to 360°?

### Tip:
In a parallelogram, if one angle is known, you can always find the others because of the supplementary and equality properties of opposite and adjacent angles.

Find the values of x, y & z in the given parallelogram.

Solve the problem of finding unknown angles x, y, and z in a parallelogram using the properties of parallelograms and supplementary angles. Detailed explanation provided for Grade 7-9 students.

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