How many vertices does a convex polyhedron have if it has 14 faces and 24 edges?

A) 8

B) 11

C) 12

D) 10

The correct answer is C) 12

Euler's formula states that the number of vertices subtracted by the number of edges and added to the number of faces of a polyhedron always equals 2:

V - E + F = 2

We have 24 edges and 14 faces:

V - 24 + 14 = 2

Combining like terms,

V - 10 = 2

Add 10 to both sides:

V - 10 + 10 = 2 + 10

V = 12