Answer:
![The \ total \ number \ of \ distinct \ diagonals \ in \ a \ polygon \ with \ n \ sides= \dfrac{n \times (n - 3)}{2}](https://tex.z-dn.net/?f=The%20%5C%20total%20%5C%20number%20%5C%20of%20%5C%20distinct%20%5C%20diagonals%20%5C%20in%20%5C%20a%20%5C%20polygon%20%5C%20with%20%5C%20n%20%5C%20sides%3D%20%5Cdfrac%7Bn%20%5Ctimes%20%28n%20-%203%29%7D%7B2%7D)
Step-by-step explanation:
A diagonal is defined in geometry as a line connecting to two non adjacent vertices.
Therefore, the minimum number of sides a polygon must have in order to have a diagonal n - 3 sides as the 3 comes from the originating vertex and the other two adjacent vertices
Given that the polygon has n sides, the number of diagonals that can be drawn from each of those n sides gives the total number of diagonals as follows;
Total possible diagonals = n × (n - 3)
However, half of the diagonals drawn within the polygon are the same diagonals drawn in reverse. Therefore, the total number of distinct diagonals that can be drawn in a polygon is given as follows;
![The \ total \ number \ of \ distinct \ diagonals \ in \ a \ polygon \ with \ n \ sides= \dfrac{n \times (n - 3)}{2}](https://tex.z-dn.net/?f=The%20%5C%20total%20%5C%20number%20%5C%20of%20%5C%20distinct%20%5C%20diagonals%20%5C%20in%20%5C%20a%20%5C%20polygon%20%5C%20with%20%5C%20n%20%5C%20sides%3D%20%5Cdfrac%7Bn%20%5Ctimes%20%28n%20-%203%29%7D%7B2%7D)