How many diagonals does a decogon have ? Geometry

[andytraiger]

This formula works because of this:
If you pick any vertex of the N-sided polygon you can figure out how many diagonals you can draw from that vertex. You can draw diagonals to all vertexes excluding these three: the vertex you picked and the two vertexes adjacent to it on either side. The reason the adjacent vertexes are excluded is that a line from a vertex to an adjacent vertex cannot be a diagonal since it is actually a side of the polygon! So from any vertex you can draw N-3 diagonals. And you can do this for all N of the vertexes. At first glance, it appears there are therefore N times N-3 diagonals; but this is not correct because you actually count diagonals twice each when you go through all N vertexes. Therefore, the correct answer is N*(N-3)/2.

[ydcjydcj]

9+8+7+6+5 = 35 .. cut the half of decagon and draw diagonals.. make sure these diagonals are not repeated

[foobar]

this video did not have the logic. only the formula. rare L of the channel.