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.