If a polyhedron has 10 vertices and 7 faces, find the number of edges in it.

Answer

To find the number of edges in a polyhedron with 10 vertices and 7 faces, we can use Euler's formula, which states:

\[ E = F + V - 2 \]

where:
- \( E \) is the number of edges,
- \( F \) is the number of faces,
- \( V \) is the number of vertices.

### Step-by-Step Solution:

1. **Identify the values:**
- Given:
- Number of vertices \( V = 10 \)
- Number of faces \( F = 7 \)

2. **Substitute the values into Euler's formula:**
\[ E = F + V - 2 \]
Substitute \( F = 7 \) and \( V = 10 \):
\[ E = 7 + 10 - 2 \]

3. **Perform the addition:**
\[ E = 17 - 2 \]

4. **Perform the subtraction:**
\[ E = 15 \]

Thus, the number of edges \( E \) in the polyhedron is **15**.