Find the missing angles in each parallelogram.

To find the missing angles in a parallelogram, we use two main rules:
1. Opposite angles are equal. (The angle across from another one is the same size).
2. Consecutive angles add up to $180^\circ$. (Angles that are next to each other form a "C" or "U" shape and sum to 180).
3. The total sum of all four angles is always $360^\circ$.

Here is the step-by-step solution for each problem:

1)
* We are given $115^\circ$.
* Angle $z$ is opposite to $115^\circ$, so $z = 115^\circ$.
* Angle $x$ is next to $115^\circ$. They must add to $180^\circ$. So, $x = 180 - 115 = 65^\circ$.
* Angle $y$ is opposite to $x$, so $y = 65^\circ$.
* Answer: $x = 65^\circ, y = 65^\circ, z = 115^\circ$

2)
* We are given $50^\circ$.
* Angle $x$ is opposite to $50^\circ$, so $x = 50^\circ$.
* Angle $y$ is next to $50^\circ$. So, $y = 180 - 50 = 130^\circ$.
* Angle $z$ is opposite to $y$, so $z = 130^\circ$.
* Answer: $x = 50^\circ, y = 130^\circ, z = 130^\circ$

3)
* We are given $121^\circ$.
* Angle $y$ is opposite to $121^\circ$, so $y = 121^\circ$.
* Angle $x$ is next to $121^\circ$. So, $x = 180 - 121 = 59^\circ$.
* Angle $z$ is opposite to $x$, so $z = 59^\circ$.
* Answer: $x = 59^\circ, y = 121^\circ, z = 59^\circ$

4)
* We are given $95^\circ$.
* Angle $y$ is opposite to $95^\circ$, so $y = 95^\circ$.
* Angles $x$ and $z$ are next to $95^\circ$. So, $x = 180 - 95 = 85^\circ$ and $z = 180 - 95 = 85^\circ$.
* Answer: $x = 85^\circ, y = 95^\circ, z = 85^\circ$

5)
* We are given $40^\circ$.
* Angle $x$ is opposite to $40^\circ$, so $x = 40^\circ$.
* Angles $y$ and $z$ are next to $40^\circ$. So, $y = 180 - 40 = 140^\circ$ and $z = 180 - 40 = 140^\circ$.
* Answer: $x = 40^\circ, y = 140^\circ, z = 140^\circ$

6)
* We are given $67^\circ$.
* Angle $z$ is opposite to $67^\circ$, so $z = 67^\circ$.
* Angles $x$ and $y$ are next to $67^\circ$. So, $x = 180 - 67 = 113^\circ$ and $y = 180 - 67 = 113^\circ$.
* Answer: $x = 113^\circ, y = 113^\circ, z = 67^\circ$

7)
* We are given $72^\circ$.
* Angle $x$ is opposite to $72^\circ$, so $x = 72^\circ$.
* Angles $y$ and $z$ are next to $72^\circ$. So, $y = 180 - 72 = 108^\circ$ and $z = 180 - 72 = 108^\circ$.
* Answer: $x = 72^\circ, y = 108^\circ, z = 108^\circ$

8)
* We are given $128^\circ$.
* Angle $y$ is opposite to $128^\circ$, so $y = 128^\circ$.
* Angles $x$ and $z$ are next to $128^\circ$. So, $x = 180 - 128 = 52^\circ$ and $z = 180 - 128 = 52^\circ$.
* Answer: $x = 52^\circ, y = 128^\circ, z = 52^\circ$

9)
* We are given $91^\circ$.
* Angle $y$ is opposite to $91^\circ$, so $y = 91^\circ$.
* Angles $x$ and $z$ are next to $91^\circ$. So, $x = 180 - 91 = 89^\circ$ and $z = 180 - 91 = 89^\circ$.
* Answer: $x = 89^\circ, y = 91^\circ, z = 89^\circ$

Final Answer:
1) $x = 65^\circ, y = 65^\circ, z = 115^\circ$
2) $x = 50^\circ, y = 130^\circ, z = 130^\circ$
3) $x = 59^\circ, y = 121^\circ, z = 59^\circ$
4) $x = 85^\circ, y = 95^\circ, z = 85^\circ$
5) $x = 40^\circ, y = 140^\circ, z = 140^\circ$
6) $x = 113^\circ, y = 113^\circ, z = 67^\circ$
7) $x = 72^\circ, y = 108^\circ, z = 108^\circ$
8) $x = 52^\circ, y = 128^\circ, z = 52^\circ$
9) $x = 89^\circ, y = 91^\circ, z = 89^\circ$