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

2 Answers
Jan 27, 2017

You cannot draw diagonals to the vertex itself as well as two adjacent vertices and hence you can draw 55 diagonals from the vertex.

Explanation:

You cannot draw diagonals to the vertex itself as well as two adjacent vertices and hence you can draw 55 diagonals from the vertex.
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Feb 7, 2017

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:
enter image source here