In the diagram, there is an object with 6 triangular faces. On each corner there is a number (two are shown). The sum of the numbers on the corners of each triangle is the same. What is the sum of all 5 numbers?

17

Step-by-step explanation:

Let the two "middle" vertexes be x1 and x2, and let the "lower" vertex be y. We know that

Therefore x1=x2. We'll call that value just x.

But now we have to be careful, because

Simplifying we can get the value of x:

Now, substituting back in, we get

So, the sum of all vertexes is equal to