This image shows a quadrilateral with two known interior angles, $100^\circ$ and $105^\circ$, and two unknown angles labeled $x$ and $y$. To find the values of $x$ and $y$, we can use the property that the sum of the interior angles of any quadrilateral is $360^\circ$.

Step-by-Step Solution

1. The sum of all interior angles in a quadrilateral is $360^\circ$.

   So, $x + 100^\circ + y + 105^\circ = 360^\circ$

2. Simplify the equation: $x + y + 205^\circ = 360^\circ$

3. Subtract $205^\circ$ from both sides: $x + y = 155^\circ$

4. Since we don't have additional information to determine $x$ and $y$ individually, we can only conclude that: $x + y = 155^\circ$

To determine the exact values of $x$ and $y$, more information about the relationship between $x$ and $y$ would be required (e.g., if it’s a trapezoid with parallel sides, or if any sides are equal).

Would you like more details on solving similar problems, or do you have any specific questions?

Related Questions

1. How do we find individual angles in quadrilaterals with additional properties, like parallel sides?
2. What are the properties of different types of quadrilaterals (e.g., parallelograms, trapezoids)?
3. How can we use exterior angles to solve for unknown angles in polygons?
4. What methods are useful for finding missing angles in polygons with more than four sides?
5. How does angle sum differ between convex and concave quadrilaterals?

Tip: Remember that the sum of interior angles in a polygon with $n$ sides is $(n - 2) \times 180^\circ$.