The number of diagonals in a polygon of m sid | vedclass

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Question

(C) To find the number of diagonals in a polygon with $m$ sides,we first consider the total number of ways to connect any two vertices,which is given

Vedclass · Accepted Answer

$\frac{1}{2}m(m - 3)$

Vedclass · Answer

(C) To find the number of diagonals in a polygon with $m$ sides,we first consider the total number of ways to connect any two vertices,which is given by $^mC_2$.This includes the $m$ sides of the polygon.Since diagonals are lines connecting non-adjacent vertices,we subtract the number of sides from the total number of connections.Number of diagonals = $^mC_2 - m$$= \frac{m(m - 1)}{2} - m$$= \frac{m(m - 1) - 2m}{2}$$= \frac{m^2 - m - 2m}{2}$$= \frac{m(m - 3)}{2}$.

The number of diagonals in a polygon of $m$ sides is

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