The image depicts a circle with two pairs of congruent right triangles inside it. Each triangle has two 90° angles at their vertices, and the sides opposite these angles are marked as equal, both measuring 12 units. We are asked to find the angle labeled $x$ (which appears to be at the circumference of the circle).

Steps to solve:

1. Understand the symmetry of the diagram:

   • The triangles are inscribed in the circle, and the angles at the center of the circle are 90°, meaning the line segments are radii of the circle.
   • The entire arc of the circle is divided into equal parts by the central angles, meaning the shape has symmetry.

2. Recognize the property of cyclic quadrilaterals: The quadrilaterals formed are cyclic (their vertices lie on the circumference). A key property is that opposite angles of a cyclic quadrilateral sum to 180°.

3. Calculate angle $x$: The two angles at the center (both 90°) divide the circle evenly into two arcs. The sum of the angles subtended by a diameter at the circumference is always 90°. Since each angle at the circumference subtended by the same arc will be equal, and the right angles at the center dictate the division, we can conclude that the angle $x$ is 90°.

Thus, the value of $x$ is $\boxed{90^\circ}$.

Would you like further details on this, or have any other questions?

Here are some related questions for deeper exploration:

1. What is a cyclic quadrilateral, and how do its properties help in circle geometry?
2. Can you explain why the angle subtended by the diameter is always 90°?
3. What are other properties of inscribed angles in a circle?
4. How can symmetry be used to solve problems in geometry?
5. What would change in this problem if the triangles were not isosceles?

Tip:

In circle geometry, always pay attention to inscribed angles and central angles; they often follow fixed relationships, which can simplify the problem-solving process.