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To solve for angle \( x \) in the given diagram:

1. **Understanding the Geometry**:
   - We see that there are 3 squares aligned between two parallel lines.
   - The angle of 40° is at one of the vertices of the first square.
   - The angle of 125° is given at the vertex between the first and second squares.
   - The angle of 35° is given at the vertex between the second and third squares.
   - We need to determine the measure of angle \( x \) at the third square, which is situated between the right side parallel line and the adjacent square.

2. **Observing the Parallel Line Configuration**:
   The squares are between two parallel lines. At each junction between squares or squares and lines, the angles formed are related by the fact that the squares are regular quadrilaterals, meaning their internal angles are 90°.

3. **Calculation**:
   At the vertex where each square meets, the angles can be calculated using the property that the internal angles at any vertex of a square add up to 360°.

   For the first vertex:
   \[
   40^\circ + 90^\circ + 125^\circ = 255^\circ
   \]
   The remaining angle is:
   \[
   360^\circ - 255^\circ = 105^\circ
   \]
   For the second vertex:
   \[
   125^\circ + 90^\circ + 35^\circ = 250^\circ
   \]
   The remaining angle is:
   \[
   360^\circ - 250^\circ = 110^\circ
   \]

4. **Finding Angle \( x \)**:
   Since the squares are positioned symmetrically between the parallel lines, the geometry and the balance of internal angles in each square mean that \( x \) should balance out the remaining space with the adjacent angles.

Therefore, angle \( x \) is \( 110^\circ \).

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Would you like more details on any specific steps, or clarifications?

Here are 5 related questions to expand on the topic:

1. How do parallel lines influence angle calculations in this context?
2. Why are square angles always 90°, and how does that affect adjacent angles?
3. How would this problem change if the shapes between the lines were rectangles instead of squares?
4. Can this method be used for calculating angles between other regular polygons?
5. What are the properties of quadrilaterals in different geometric configurations?

**Tip**: When working with parallel lines and polygons, always remember to use the angle sum properties effectively, such as the fact that angles around a point sum up to 360°.

As shown in the diagram, there lie 3 squares between 2 parallel lines such that each pair (line, square) or (square, square) just meet at a vertex. Find the measure of angle x in degrees.

Learn how to find the measure of angle x in a diagram involving 3 squares positioned between two parallel lines. This problem covers key geometric concepts, including the properties of squares, parallel lines, and angle sums. Suitable for students in Grades 8-10.

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