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  4. The number of diagonals that can be drawn by joining the vertices of an octagon, is

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Q. The number of diagonals that can be drawn by joining the vertices of an octagon, is

Bihar CECEBihar CECE 2010

Solution:

The total number of lines obtained by joining 8 vertices of octagon
$ ={{\,}^{8}}{{C}_{2}}=\frac{8.7}{2}=28 $
But out of these 28 lines, 8 are sides and remaining are diagonals. Hence, the number of diagonals $ =28-8=20 $