Q. 43.8( 6 Votes )

In regular polygo

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’.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses

In regular polygoKerala Board Mathematics Part-2

For squares, is aKerala Board Mathematics Part-2

In rectangles of Kerala Board Mathematics Part-2

Prove that for eqKerala Board Mathematics Part-2

A fixed volume ofKerala Board Mathematics Part-2

In triangles of tKerala Board Mathematics Part-2