From the image, we can observe a parallelogram with angles and a diagonal. The given angles are:

• Angle adjacent to $x$ is 30° (top-right corner)
• Angle adjacent to $y$ is 100° (bottom-left corner)
• Angle adjacent to the 100° is also 100° (bottom-right corner)

The diagonal splits the parallelogram into two triangles, creating an internal angle opposite the diagonal at the top-left of 100°. We are asked to find the values of $x$ and $y$.

Approach:

1. Triangle 1: The triangle at the top (with the angles involving $x$).

   • One angle is given as 30°.
   • Another angle is $x$.
   • The sum of angles in a triangle is always 180°. Hence, we can calculate $x$ as follows: $100^\circ + 30^\circ + x = 180^\circ$ Solving for $x$: $x = 180^\circ - 130^\circ = 50^\circ$

2. Triangle 2: The triangle at the bottom (with the angles involving $y$).

   • One angle is given as 100°.
   • Another angle is $y$.
   • Using the sum of angles in a triangle: $100^\circ + 100^\circ + y = 180^\circ$ Solving for $y$: $y = 180^\circ - 200^\circ = -20^\circ$ However, this result for $y$ is incorrect, likely due to an interpretation issue in labeling or assumption about the shape. If the figure is a parallelogram, the opposite angles should match, meaning $y$ might involve other assumptions. We should carefully revise the figure for any misinterpretations of parallelogram properties.

Would you like me to further analyze or recalculate based on a specific assumption? Let me know if any additional clarifications are needed!

Related questions:

1. How are angles in a parallelogram related, and how does that apply here?
2. What are the properties of diagonals in a parallelogram regarding angle bisectors?
3. How can we apply the sum of angles in a triangle to more complex figures?
4. Can supplementary angles be used in parallelograms, and how does this affect internal triangles?
5. How does the sum of adjacent angles in polygons help solve this?

Tip: Always verify the shape’s properties (like symmetry) before calculating unknown angles.