This image displays a quadrilateral with two given interior angles, 100° and 105°. To find the values of $x$ and $y$, we can use the fact that the sum of the interior angles in any quadrilateral is always $360^\circ$.

Let's break down the solution:

1. Let the four angles of the quadrilateral be $x$, $100^\circ$, $105^\circ$, and $y$.
2. The sum of these angles is: $x + 100^\circ + 105^\circ + y = 360^\circ$
3. Simplifying, we get: $x + y + 205^\circ = 360^\circ$
4. Subtract $205^\circ$ from both sides: $x + y = 155^\circ$

So, we now know that: $x + y = 155^\circ$

To find individual values of $x$ and $y$, we would need additional information, such as if the quadrilateral has any symmetry (e.g., if it is an isosceles trapezoid). Without this information, we cannot uniquely determine $x$ and $y$ but only state that their sum is $155^\circ$.

Would you like further explanation on this solution, or do you have any additional details about the shape?

Here are some related questions to consider:

1. How do we find the sum of interior angles for polygons with more than four sides?
2. What methods exist to determine individual angle values if given partial information in a quadrilateral?
3. How do properties like parallel sides in a trapezoid affect angle calculations?
4. What is the relationship between exterior and interior angles in polygons?
5. Can symmetry in a shape provide additional information to solve for unknown angles?

Tip: Always look for special properties or symmetry in a quadrilateral, as they can simplify calculations by giving additional constraints.