Problem Explanation:

The figure consists of two squares that are arranged such that their bases form angles $37^\circ$ and $23^\circ$ with the horizontal. The task is to find the value of $x$, the angle formed between the squares at their intersection.

Solution:

1. Key Geometry Property:

   • The interior angles of a square are all $90^\circ$.
   • Since the two squares meet along their sides, the angle $x$ depends on the angles formed by the rotation of the squares relative to the horizontal.

2. Angle Relationship:

   • The angle $x$ is the supplement of the sum of the two base angles ($37^\circ$ and $23^\circ$): $x = 180^\circ - (37^\circ + 23^\circ)$

3. Calculation: $x = 180^\circ - 60^\circ = 120^\circ$

Final Answer:

$x = 120^\circ$

Would you like further clarification or a detailed step-by-step breakdown?

Related Questions:

1. How do supplementary angles work in geometry?
2. What are the properties of squares that are useful in angle calculations?
3. How can we verify this result using alternate geometry methods?
4. What happens to the angle $x$ if one square is rotated differently?
5. Can this method be applied to other polygons besides squares?

Tip:

When working with angles, always verify if they are complementary, supplementary, or part of a specific geometric property!