# you are given a polygon with n=50 sides. how many diagonals does this polygon have? show all work.

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### 1 Answer

A diagonal is a line joining two nonconsecutive vertices of a polygon. The polygon here has 50 sides. A polygon that has 50 sides has fifty vertices.

From each vertex we can draw a diagonal to 48 other vertices.

But the diagonal drawn from a vertex to another, and that from the other vertex to the one we started with, is the same. This reduces the total number of diagonals to half.

The total number of diagonals is 50*48/2 = 1200

**A polygon with 50 sides has 1200 diagonals.**