Question

If all possible diagonals from a vertex of an n sided polygon are drawn, then the number of triangles formed will be

• A. $n-1$
• B. $n-2$
• C. $n-3$
• D. $n-4$

Answer 1

The correct option is B $n-2$

The triangles are created by drawing the diagonals from one vertex to all the others. Since there would be no diagonal drawn back to itself, and the diagonals to each adjacent vertex would lie on top of the adjacent sides, the number of diagonals from a single vertex is three less the number of sides, or $n-3$. The number of triangles is one more than that, so $n-2.$