There are 10 vertices in a decagon.
Now by joining two vertices, we get a side of decagon or a diagonal.
Hence, the number of the line segment by joining of vertices of decagon = number of ways taking 2 points out of 10 points
= 10C2 = (10(10 - ))/2!
Now, there are 10 sides of decagon in 10C2 line segment
∴ Required number of diagonals
Hence, the number of diagonals is 35.