Question

Number of diagonals in the polygon can be

• A. Greater than the number of vertices
• B. Smaller than the number of vertices
• C. Equal to the number of vertices in the polygon.
• D. None

Answer 1

Answer: (A), (B), (C)

Equal to the number of vertices in the polygon.

Number of diagonals can be greater than, equal to or less than the number of vertices of the polygon.
we can see the examples also-

In the above polygon $ABCD$, total vertices are $4$ and diagonals are $2$ in number so here number of diagonals are less than the number of vertices.

Now, let us see the other example-

In polygon $PQRST$, there are total $5$ diagonals and also $5$ vertices so here the number of diagonals is equal to the number of verticers in the polygon.

And let us see one more example-

In the polygon $KLMNOP$, there are total $6$ vertices and $9$ diagonals so here the number of diagonals is greater than the number of vertices of the polygon.

So, the number of diagonals can be equal to less than or greater than the number of vertices in the polygon.

Hence, option $\left(a\right)$, $\left(b\right)$ and $\left(c\right)$ correct.