Solution:

To find the number of diagonals of an n-sided polygon, we need to understand what a diagonal is and how many diagonals are present in a polygon.

What is a diagonal?

A diagonal is a line segment that connects two non-adjacent vertices of a polygon.

How many diagonals are present in a polygon?

To count the number of diagonals in a polygon, we need to consider each vertex of the polygon and count the number of diagonals that can be drawn from that vertex.

For example, consider a square.

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There are four vertices in the square. If we start with the top-left vertex and count the number of diagonals that can be drawn from that vertex, we get two diagonals. Similarly, if we count from the top-right vertex, we get two diagonals. If we count from the bottom-left vertex, we get two diagonals, and if we count from the bottom-right vertex, we get two diagonals. So, in total, there are eight diagonals in a square.

This method works for any polygon. For an n-sided polygon, we have n vertices, and if we count the number of diagonals that can be drawn from each vertex, we get:

- From each vertex, we can draw n-3 diagonals (because we cannot draw a diagonal to the adjacent vertices or to itself).
- Since there are n vertices, the total number of diagonals in an n-sided polygon is:

n(n-3)/2

Therefore, the correct option is (D) n(n-3)/2.