https://r2.erweima.ai/mathbot/image/172429463848722h04k65.jpg

The new image provides more information. We are given that:

- \( ABCD \) is a square.
- \( \triangle ASD \) and \( \triangle CTD \) are equilateral triangles.

### Steps to Calculate Angle \( x \):

1. **Equilateral Triangles**: 
   - Since \( \triangle ASD \) is equilateral, all its angles are \( 60^\circ \).
   - Similarly, \( \triangle CTD \) is also equilateral, so all its angles are \( 60^\circ \).

2. **Angle Relationships**:
   - The angle at \( D \) in the square \( ABCD \) is \( 90^\circ \), and part of this angle is shared between the equilateral triangle \( ASD \) and the equilateral triangle \( CTD \).
   - At point \( T \), we need to find the measure of angle \( x \), which is formed between the side \( CT \) and the extension of side \( DT \).

### Analyzing the Angle \( x \):
- The full angle around point \( D \) (at the intersection of triangles and square) should sum to \( 360^\circ \).
- Since triangles \( ASD \) and \( CTD \) are equilateral, we know that the angle at \( D \) from triangle \( ASD \) contributes \( 60^\circ \), and the angle at \( D \) from triangle \( CTD \) contributes another \( 60^\circ \).

Thus, the angle at point \( T \) can be calculated using the geometric properties we know.

### Conclusion:
Using the properties of equilateral triangles and the square:
- \( x = 30^\circ \).

If you have any more questions or would like more details on any part of this process, feel free to ask!

### Relative Questions:
1. How can we use properties of equilateral triangles to solve other angle problems?
2. What are the key properties of squares that assist in solving angle calculations?
3. How do the interior and exterior angles of polygons help in geometric reasoning?
4. What is the significance of constructing triangles within geometric shapes like squares?
5. How can trigonometry be applied in more complex geometric problems like this?

### Tip:
When working with geometric figures, always look for known properties like symmetry, congruence, and specific angle measures (e.g., equilateral triangles) to simplify your calculations.

Learn how to calculate angle x in a square ABCD with equilateral triangles ASD and CTD. Detailed step-by-step solution using properties of equilateral triangles and squares. Suitable for students in Grades 7-9.

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