The problem asks to find the values of the unknown angles $x, y, z$ in the two given parallelograms.

1. Problem Description

The problem asks to find the values of the unknown angles $x, y, z$ in the two given parallelograms.

2. Solution Steps

(i) For the first parallelogram:

In a parallelogram, adjacent angles are supplementary, meaning they add up to 180 degrees.

Thus, $x + 100^{\circ} = 180^{\circ}$

$x = 180^{\circ} - 100^{\circ} = 80^{\circ}$

Also, opposite angles in a parallelogram are equal.

$y = 100^{\circ}$

$z = x = 80^{\circ}$

(ii) For the second parallelogram:

In a parallelogram, adjacent angles are supplementary, meaning they add up to 180 degrees.

$50^{\circ} + y = 180^{\circ}$

$y = 180^{\circ} - 50^{\circ} = 130^{\circ}$

Also, opposite angles in a parallelogram are equal.

$x = 50^{\circ}$

$z$ is an exterior angle of the parallelogram. $z$ and $x$ form a linear pair. Thus,

$z + x = 180^{\circ}$

$z = 180^{\circ} - x = 180^{\circ} - 50^{\circ} = 130^{\circ}$

3. Final Answer

(i) $x = 80^{\circ}$, $y = 100^{\circ}$, $z = 80^{\circ}$

(ii) $x = 50^{\circ}$, $y = 130^{\circ}$, $z = 130^{\circ}$