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The expression for the number of diagonals that we can make from one vertex of a n sided polygon is:
(a) 2n + 1
(b) n - 2
(c) 5n + 2
(d) n - 3

Solution:

We have to write an expression for the number of diagonals that we can make from one vertex of a n sided polygon.

Consider triangle,

A triangle has three sides.

In a triangle, there is no diagonal

So, the number of diagonals is zero.

From the option,

1) 2n + 1

Put n = 3,

2n + 1 = 2(3) + 1

= 7

Therefore, option a is incorrect

2) n - 2

Put n = 3,

n - 2 = 3 - 2

= 1

Therefore, option b is incorrect.

3) 5n + 2

Put n = 3,

5n + 2 = 5(3) + 2

= 15 + 2

= 17

Therefore, option c is incorrect.

4) n - 3

Put n = 3,

n - 3 = 3 - 3

= 0

Therefore, option d is correct.

Similarly, for quadrilateral n = 4, the number of diagonals from a vertex is 1.

So, n - 3 = 4 - 3 = 1

For pentagon n = 5, the number of diagonals from a vertex is 2.

So, n - 3 = 5 - 3 = 2

Therefore, the required expression is n - 3.

✦ Try This: How many triangles can be made if all the diagonals from a vertex of a 10 sided polygon are drawn?

☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 12

NCERT Exemplar Class 7 Maths Chapter 10 Problem 15

Summary:

The expression for the number of diagonals that we can make from one vertex of a n sided polygon is n - 3.

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