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# If all of the diagonals are drawn from a vertex of an n-gon, how many triangles are formed?

n - 2

n - 1

n

n + 1

**Solution:**

We know that the number of triangles which are formed by connecting one of the vertices to the rest of the vertices is equal to n - 2.

For example,

For the quadrilateral, there are 4 sides

So we get 4 - 2 = 2

Here 2 triangles can be formed.

For a pentagon, there are 5 sides

So we get 5 - 2 = 3

Here 3 triangles can be formed.

Therefore, n - 2 triangles are formed.

## If all of the diagonals are drawn from a vertex of an n-gon, how many triangles are formed?

**Summary:**

If all of the diagonals are drawn from a vertex of an n-gon, n - 2 triangles are formed.

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