If a polyhedron has 10 faces and 8 vertices, find the number of edges in it.

Answer

To find the number of edges in a polyhedron with 10 faces and 8 vertices, 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 given values**:
- Number of faces \( F = 10 \)
- Number of vertices \( V = 8 \)

2. **Substitute the values into Euler's formula**:
\[ E = F + V - 2 \]
Substitute \( F \) and \( V \):
\[ E = 10 + 8 - 2 \]

3. **Perform the addition**:
\[ E = 18 - 2 \]

4. **Perform the subtraction**:
\[ E = 16 \]

Thus, the number of edges \( E \) in the polyhedron is **16**.