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To solve this problem, we use the property of similar figures, which states that corresponding sides of similar figures are proportional. The two shapes shown are similar (having the same angles), so their corresponding side lengths are proportional.

### Given:
- Large figure: sides \( 72 \) cm and \( x \).
- Small figure: sides \( 24 \) cm and \( 6 \) cm.

### Set up the proportion:
\[
\frac{72}{24} = \frac{x}{6}
\]

### Simplify the left side:
\[
\frac{72}{24} = 3
\]

Now, substitute into the proportion:
\[
3 = \frac{x}{6}
\]

### Solve for \( x \):
\[
x = 3 \times 6 = 18
\]

### Answer:
The value of \( x \) is \( \boxed{18} \), which corresponds to option **C**.

Would you like more details or have any questions?

### Related Questions:
1. What are the properties of similar figures?
2. How do you determine if two figures are similar?
3. How can we use proportions in real-world applications?
4. What happens if one of the given side lengths is unknown?
5. How can this method be applied to three-dimensional figures?

### Tip:
Always check if figures are similar by comparing their angles and corresponding side ratios.

Use similar figures to determine the value of x, given two trapezoids with angles of 45° and side lengths 72 cm and x for the larger one, and 24 cm and 6 cm for the smaller one.

Learn how to solve for x in a geometry problem involving two similar trapezoids with 45° angles. The given side lengths are 72 cm, 24 cm, 6 cm, and x. This solution involves the use of proportional reasoning and similar figures, suitable for students in Grades 8-10.

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