Find the number of sides in a polygon if it has 65 diagonals.
11
15
12
13
In this case, let's say that the polygon has n sides. Therefore, there will also be 'n' vertices.
If we connect any of these n points to form a line, the result will either be a diagonal or a side of the polygon.
Thus, there are methods in total to choose two points from a total of n points.
The total number of lines formed using n vertices = Number of diagonal + Number of sides.
We can write
Rearranging the equation to get,
Solving the quadratic equation to get,
n = 13 and n = -10
The value of n cannot be negative.
Therefore, the number of sides in a polygon is 13.
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