Answer :

Let us consider a regular polygon.

We know how to calculate the sum of all its interior angles.

s = 180 (n – 2)

Where, s = sum

N is the number of sides of the regular polygon

Let us use this formula for a triangle:

For a triangle, n = 3

So, s = 180 × (3 – 2)

= 180 × 1

= 180

Let us use this formula for a square:

For a square, n = 4

So, s = 180 × (4 – 2)

= 180 × 2

= 360

Let us use this formula for a pentagon:

For a square, n = 5

So, s = 180 × (5 – 2)

= 180 × 3

= 540

Let us tabulate the results:

From the above table we can see that s/n is not a constant. So, s is not proportional to n.

Let us modify the formula

Let s = 180 × m

Where s = sum

M = (n-2)

N is the number of side of the regular polygon

We can see that s is proportional to m. The constant of proportionality is 180

In ordinary language, we can say this:

The sum of interior angle of a regular polygon is proportional to ‘2 less than the number of sides’.

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