The image shows a polygon with angles labeled as follows:

1. $100^\circ$
2. $60^\circ$
3. $130^\circ$
4. $x^\circ$
5. $y^\circ$

The interior angles of a polygon sum to $(n-2) \times 180^\circ$, where $n$ is the number of sides.

This polygon has 5 sides (a pentagon), so the sum of its interior angles is:

$(5 - 2) \times 180^\circ = 3 \times 180^\circ = 540^\circ$

Now, let's sum the known angles and solve for the missing ones $x^\circ$ and $y^\circ$:

$100^\circ + 60^\circ + 130^\circ + x^\circ + y^\circ = 540^\circ$

Simplifying this equation:

$290^\circ + x^\circ + y^\circ = 540^\circ$

$x^\circ + y^\circ = 540^\circ - 290^\circ = 250^\circ$

Without more information (like additional given angles or relationships between $x$ and $y$), we can only say that $x + y = 250^\circ$. If there's any specific relationship between these angles given by the diagram or problem context, that would help determine the individual values of $x$ and $y$.

Would you like more details or have any questions? Here are some related questions:

1. How do you calculate the sum of interior angles for different polygons?
2. What are exterior angles, and how do they relate to interior angles in polygons?
3. How can you determine the individual angles if more information is provided?
4. What is the general formula for the sum of exterior angles of any polygon?
5. How does the number of sides in a polygon affect the sum of its interior angles?

Tip: When working with polygons, always start by calculating the sum of the interior angles. This foundational step helps in finding unknown angles when partial information is given.