The diagram you've provided shows a quadrilateral with specific angle relationships. To solve for the values of $x$, $y$, and $z$, we need to consider both the parallel lines and the internal angle relationships.

Observations:

• The figure appears to show a parallelogram, given the pairs of parallel lines marked by arrows.
• The angles at points $A$, $B$, and $C$ are labeled $x^\circ$, $y^\circ$, and 104°, respectively.
• The exterior angle at point $D$ is labeled $z^\circ$.

Key facts:

• In a parallelogram, consecutive angles are supplementary, meaning they sum to $180^\circ$.
• The exterior angle $z$ is supplementary to the interior angle at point $C$ because the exterior angle of any polygon is supplementary to its adjacent interior angle.

Step-by-Step Solution:

1. Angle $y$ at Point $B$: Since angle $B$ and angle $C$ are consecutive angles in a parallelogram, they must add up to $180^\circ$. So, $y^\circ + 104^\circ = 180^\circ$ $y = 180^\circ - 104^\circ = 76^\circ$

2. Angle $x$ at Point $A$: Angle $A$ and angle $D$ are also consecutive angles in the parallelogram, so they too must sum to $180^\circ$. Since angle $D$ is equal to $x$ due to the symmetry of the parallelogram, $x = y = 76^\circ$

3. Exterior Angle $z$ at Point $D$: The exterior angle $z$ is supplementary to the interior angle at point $C$, which is 104°. Therefore, $z^\circ + 104^\circ = 180^\circ$ $z = 180^\circ - 104^\circ = 76^\circ$

Final Answers:

• $x = 76^\circ$
• $y = 76^\circ$
• $z = 76^\circ$

Would you like further details on any step?

Here are five related questions for further exploration:

1. What are the properties of a parallelogram regarding angles and sides?
2. How do you prove that consecutive angles in a parallelogram are supplementary?
3. What is the sum of the interior angles of any quadrilateral?
4. How does an exterior angle relate to the interior angle of any polygon?
5. Can this approach be applied to non-parallel quadrilaterals?

Tip: In any polygon, the exterior angle is always supplementary to its adjacent interior angle!