Parts of a pentagon have areas $x,y,z$ as shown in the picture. Given the area $x$, find the areas $y$ and $z$ and the area of the entire pentagon.
[img]https://services.artofproblemsolving.com/download.php?id=YXR0YWNobWVudHMvOS9mLzM5NjNjNDcwY2ZmMzgzY2QwYWM0YzI1NmYzOWU2MWY1NTczZmYxLnBuZw==&rn=U2NyZWVuIFNob3QgMjAyMS0wNC0wOCBhdCA0LjMwLjU1IFBNLnBuZw[/img]
1. **Identify the relationship between the areas:**
   - The pentagon is divided into smaller regions with areas \(x\), \(y\), and \(z\).
   - The smaller pentagon with area \(x\) is similar to the entire pentagon.

2. **Use the properties of similar polygons:**
   - If two polygons are similar, the ratio of their areas is the square of the ratio of their corresponding side lengths.
   - Let the side length of the smaller pentagon be \(a\) and the side length of the larger pentagon be \(A\).
   - The ratio of the side lengths is \(\frac{a}{A}\).

3. **Express the area of the smaller pentagon in terms of the larger pentagon:**
   - The area of the smaller pentagon is \(x\).
   - The area of the larger pentagon is \(A^2\).
   - Since the smaller pentagon is similar to the larger pentagon, the ratio of their areas is \(\left(\frac{a}{A}\right)^2\).
   - Therefore, \(x = \left(\frac{a}{A}\right)^2 \cdot A^2\).

4. **Determine the areas \(y\) and \(z\):**
   - The areas \(y\) and \(z\) are parts of the larger pentagon that are not part of the smaller pentagon.
   - Since the smaller pentagon is surrounded by five regions of area \(y\) and five regions of area \(z\), we can write:
     \[
     \text{Total area of the larger pentagon} = x + 5y + 5z
     \]
   - Let the total area of the larger pentagon be \(A_{\text{total}}\).

5. **Express the total area in terms of \(x\), \(y\), and \(z\):**
   - Since the smaller pentagon is similar to the larger pentagon, the total area can be written as:
     \[
     A_{\text{total}} = x + 5y + 5z
     \]

6. **Solve for \(y\) and \(z\):**
   - Without specific values for \(x\), \(y\), and \(z\), we can only express the relationships between these areas.
   - If we assume that the areas \(y\) and \(z\) are equal, we can write:
     \[
     y = z
     \]
   - Therefore, the total area becomes:
     \[
     A_{\text{total}} = x + 5y + 5y = x + 10y
     \]

7. **Conclusion:**
   - The areas \(y\) and \(z\) can be expressed in terms of the total area and the area \(x\):
     \[
     y = z = \frac{A_{\text{total}} - x}{10}
     \]

The final answer is \( \boxed{ y = z = \frac{A_{\text{total}} - x}{10} } \)