Question

How many diagonals can you draw from the vertex of an octagon?

Answer 1

You cannot draw diagonals to the vertex itself as well as two adjacent vertices and hence you can draw `5` diagonals from the vertex.

Explanation:

You cannot draw diagonals to the vertex itself as well as two adjacent vertices and hence you can draw `5` diagonals from the vertex.

Answer 2

5

Explanation:

Start with ONLY one vertex. The diagonals will extend from this vertex ONLY.

Considering that a diagonal can not extend to the vertex directly adjacent to it (because it just traces the side), we eliminate two possibilities (8 - 2 = 6 diagonals).

Also, you can not extend a diagonal from a vertex to that same vertex. Therefore, we eliminate another possibility. (6 - 1 = 5 diagonals).

Here's a visual: